{"id":2213,"date":"2023-10-02T10:57:59","date_gmt":"2023-10-02T10:57:59","guid":{"rendered":"http:\/\/localhost\/ecole9ja\/?p=2213"},"modified":"2023-10-02T11:02:26","modified_gmt":"2023-10-02T11:02:26","slug":"week-6-and-7-ss1-second-term-mathematics-notes","status":"publish","type":"post","link":"https:\/\/ecolebooks.com\/nigeria\/posts\/week-6-and-7-ss1-second-term-mathematics-notes\/","title":{"rendered":"Week 6 and 7 &#8211; SS1 Second Term Mathematics Notes"},"content":{"rendered":"<p>\u00a0<strong>WEEK SIX<br \/>\n<\/strong><strong>Review of the first half term&#8217;s work and periodic test<br \/>\n<\/strong><strong>WEEK SEVEN<br \/>\n<\/strong><strong>TOPIC: TRIGONOMETRIC RATIOS<br \/>\n<\/strong><strong>CONTENT<br \/>\n<\/strong><\/p>\n<ul>\n<li>Sine,Cosine and Tangent of acute angles\n<\/li>\n<li>Use of tables of Trigonometric ratios\n<\/li>\n<li>Determination of lengths of chord using trigonometric ratios.\n<\/li>\n<li>Graph of sine and cosine for angles\n<\/li>\n<\/ul>\n<p>\u00a0<strong>Sine, Cosine and Tangent of acute angles<br \/>\n<\/strong>Given a right angled triangle, the trigonometric ratio of acute angles can be found as shown  below<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and71.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and72.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and73.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and74.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and75.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and76.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and77.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and78.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and79.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and710.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and711.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0In the figure above,  ABC is any triangle, right-angled at A<br \/>\ntan B  =  b        tan C  = c(tan : Opp)<br \/>\nc                 b          Adj<br \/>\nSin B = b   Sin C  =c  Sin ;Opp<br \/>\naaHyp<\/p>\n<p>\u00a0Cos B  = c   Cos C  =  b ( Cos : Adj)<br \/>\n\t\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and712.png\" alt=\"\"\/>aaHyp<br \/>\nInABC, B and C are complementary angles i.e B + C = 90<sup>o  <\/sup><br \/>\n\tIf B =  \u04e8  then C = 90<sup>o<\/sup> &#8211; \u04e8.<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and713.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and714.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and715.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and716.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and717.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and718.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and719.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and720.png\" alt=\"\"\/><br \/>\n\t\u00a0\u00a0\u00a0\u00a0<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and721.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and722.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and723.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0In the figure above sin \u04e8  =cos ( 90-\u04e8 )  = b<br \/>\na<br \/>\nCos \u04e8  = Sin (90- \u04e8)  = c<br \/>\na<br \/>\nNote:  Always remember SOH      CAH   TOA<br \/>\ni.e Sin \u03b8 = Opp<br \/>\nHyp<br \/>\nCos \u03b8= Adj<br \/>\nHyp<\/p>\n<p>\u00a0Tan O  =Opp<br \/>\nAdj.<\/p>\n<p>\u00a0<strong>Examples<br \/>\n<\/strong><\/p>\n<ol>\n<li>A triangle has sides 8cm and 5cm and an angle of 90<sup>o<\/sup> between them .Calculate the smallest angle of the triangle\n<\/li>\n<li>A town Y is 200km from town X in a direction 40<sup>o<\/sup>.  How far isY east of X ?\n<\/li>\n<li>In the figure below, LK  is perpendicular to  MN. Calculate&lt; MNL\n<\/li>\n<\/ol>\n<p><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and724.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and725.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and726.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and727.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and728.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and729.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and730.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and731.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and732.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and733.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and734.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and735.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and736.png\" alt=\"\"\/><\/p>\n<p>\u00a0Solutions<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and737.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and738.png\" alt=\"\"\/>(1)<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and739.png\" alt=\"\"\/><\/p>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and740.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and741.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and742.png\" alt=\"\"\/><\/p>\n<p>\u00a0tan \u03b8 =  8cm    = 1.600<br \/>\n             5cm<br \/>\n\u04e8  = tan<sup>-1<\/sup> 1.6000<br \/>\n\u04e8 = 58<sup>o<\/sup>.<br \/>\nThe 3<sup>rd<\/sup> angle in the right angled triangle above = 90<sup>o<\/sup> \u2013 58<sup>o<\/sup>  = 32.<br \/>\nHence, the smallest angle of the  given triangle = 32<sup>o<\/sup><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and743.png\" alt=\"\"\/><br \/>\n\t\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0        Y<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and744.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and745.png\" alt=\"\"\/>2)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and746.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and747.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and748.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and749.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and750.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0From the diagram drawn above the distance of Y east of X = ZY<br \/>\nUsing the right angled triangle XZY<br \/>\nSin 40<sup>o <\/sup> =ZY<br \/>\n                200km<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and751.png\" alt=\"\"\/>ZY  = 200km x sin 40<sup>o<\/sup><br \/>\n\t= 200km x 0.6428<br \/>\n= 128.56km<br \/>\n= 128.6km to 1d.p<\/p>\n<p>\u00a03)<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and752.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0In the given diagram,<br \/>\nLK       = Sin 70<sup>o<\/sup><br \/>\n\t7cm<\/p>\n<p>\u00a0LK  = 7cm x sin 70<sup>o<\/sup>  \u2026\u2026\u2026\u2026 i<br \/>\nLK  = 7cm x 0.9397<\/p>\n<p>\u00a0LK  = 6.5779cm<\/p>\n<p>\u00a0In right angled triangle  LKN<\/p>\n<p>\u00a0LK = sin MNL<br \/>\n21<\/p>\n<p>\u00a0i.e 7cm x 0.9397   = Sin MNL<br \/>\n              21cm<\/p>\n<ol>\n<li>=  Sin MNL\n<\/li>\n<\/ol>\n<p>    3<br \/>\n  0.3132   = Sin MNL<br \/>\nSin<sup>-1<\/sup>0.3132  = MNL<br \/>\n18. 290  = MNL<br \/>\ni.e  MNL =  18.3<sup>o<\/sup><\/p>\n<p>\u00a0<strong>EVALUATION<br \/>\n<\/strong>A ladder 20cm long rests against a vertical wall so that the foot of the ladder is 9m from the wall.<br \/>\n(a) Find, correct to the nearest degree, the angle that the ladder makes with the wall<br \/>\n(b) Find correct to 1.dp the height above the ground at which the upper end of the ladder touches the wall. Use of tables of trigonometric ratios.<\/p>\n<p>\u00a0<br \/>\n\u00a0<strong>Determination of lengths of chords using trigonometric ratios<br \/>\n<\/strong>Trignometric ratios can be used to find the length of chords of a given circle.  However, in some cases where angles are not given, Pythagoras theorem is used to find the lengths of chords in such cases. Pythagoras theorem is stated as follows:<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and753.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0It states that c<sup>2<\/sup> = a<sup>2<\/sup> + b<sup>2<\/sup><br \/>\n\tPythagoras theorem states that in a right angled triangle, the square of the length of the hypotenuse is equal to the sum of the square of the lengths of the other two sides.<br \/>\nExamples<\/p>\n<p>\u00a0<\/p>\n<ol>\n<li>A chord is drawn 3cm away from the centre of a circle of radius 5cm. Calculate the length of the chord.\n<\/li>\n<li>\n<div>In the figure below, O is the centre of circle, HKL.  HK = 16cm, HL = 10cm and the perpendicular from O to the HK is 4cm.  What is the length of the perpendicular from O to HL?\n<\/div>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and754.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<\/li>\n<\/ol>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<\/p>\n<ol>\n<li>Given the figure below, calculate the length of the chord AB.\n<\/li>\n<\/ol>\n<p><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and755.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and756.png\" alt=\"\"\/><br \/>\n\t\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0           58<sup>o<\/sup>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and757.png\" alt=\"\"\/>Solutions<br \/>\n1<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0      B<br \/>\nFrom the diagram above in right-angled triangle  ABO:<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and758.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and759.png\" alt=\"\"\/><br \/>\n\t AB   <sup>2<\/sup>  + 3<sup>2<\/sup>  = 5<sup>2<\/sup>  ( Pythagoras theorem)<\/p>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and760.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and761.png\" alt=\"\"\/>AB    <sup>2<\/sup>=  5<sup>2<\/sup> &#8211; 3<sup>2<\/sup><\/p>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and762.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and763.png\" alt=\"\"\/>AB    <sup>2<\/sup>  = 25 \u2013 9<\/p>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and764.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and765.png\" alt=\"\"\/>AB   <sup>2<\/sup>  = 16<\/p>\n<p>\u00a0AB      = \u221a16 = 4cm <\/p>\n<p>\u00a0Since B is the mid point of chord AC then<\/p>\n<p>\u00a0Length of chord AC = 2 x AB<br \/>\n = 2x 4cm =8cm<\/p>\n<p>\u00a02)<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and766.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and767.png\" alt=\"\"\/><br \/>\n\t\u00a0\u00a0\u00a0\u00a0<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and768.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and769.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and770.png\" alt=\"\"\/><br \/>\n\t\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0   0<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and771.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and772.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0Let the distance from O to HL= xcm<br \/>\nIn right-angled triangle OMH:<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and773.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and774.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and775.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and776.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and777.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and778.png\" alt=\"\"\/><br \/>\n\tOH   <sup>2 <\/sup> =        HM <sup>2<\/sup>   +            MO  <sup>2<\/sup><\/p>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and779.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and780.png\" alt=\"\"\/><br \/>\n\tOH  <sup>2<\/sup>=  8<sup>2<\/sup> + 4<sup>2<\/sup><\/p>\n<p>\u00a0=  64  + 16<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and781.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and782.png\" alt=\"\"\/>= 80<br \/>\n:.         OH  = \u221a80<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and783.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and784.png\" alt=\"\"\/><br \/>\n\t:.           OH   = \u221a80cm<\/p>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and785.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and786.png\" alt=\"\"\/>but   OH   = radius of the circle <\/p>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and787.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and788.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and789.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and790.png\" alt=\"\"\/><br \/>\n\ti.e r=   OH     =   OL  = \u221a80cm<br \/>\nIn right-angled triangle  ONL<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and791.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and792.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and793.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and794.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and795.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and796.png\" alt=\"\"\/><br \/>\n\tOL  <sup>2<\/sup>  =    ON <sup>2<\/sup>   +   NL <sup>2<\/sup><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and797.png\" alt=\"\"\/>i.e( \u221a80)<sup>2<\/sup> = x<sup>2 <\/sup>+ 5<sup>2<\/sup><br \/>\n\t80- 25 = x<sup>2<\/sup><br \/>\n\t55 = x<sup>2<\/sup><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and798.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and799.png\" alt=\"\"\/>Take square root of both sides<br \/>\n\u221a55   = \u221ax<sup>2<\/sup><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and7100.png\" alt=\"\"\/>\u221a55 = x = 7. 416cm<br \/>\n:. The length of the perpendicular from O to HL is 7.416cm<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and7101.png\" alt=\"\"\/><\/p>\n<p>\u00a03)<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0The perpendicular from O to AB divides the vertical angle into 2 equal parts and also divides the length of chord AB into two equal parts.<\/p>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and7102.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and7103.png\" alt=\"\"\/>In right-angled triangle ACO:<br \/>\nAC    =    Sin 29<sup>o<\/sup><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and7104.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and7105.png\" alt=\"\"\/>  OA              1<br \/>\nCross multiply<br \/>\nAC  = OA  x sin 29<sup>o<br \/>\n<\/sup>AC = 14cm x Sin 29<sup>o<br \/>\n<\/sup>AC  = 14cm  x 0. 4848<br \/>\nAC = 6.787cm<br \/>\nAB  = 2 x 6.787 cm<br \/>\nAB = 13.574cm<br \/>\n:. The length of the chord AB = 13.6cm to 1 d.p<\/p>\n<p>\u00a0<strong>EVALUATION<br \/>\n<\/strong><\/p>\n<ol>\n<li>A chord 30cm long is 20cm from the centre of a circle . Calculate the length of the chord which is 24cm from the centre .\n<\/li>\n<li>Q is 1.4km from P on a bearing 023<sup>o<\/sup>. R is 4.4 Km from P on a bearing 113<sup>o<\/sup>. Make a sketch of the positions of P, Q and R and hence, calculate QR correct to 2 s.f.\n<\/li>\n<\/ol>\n<p>\u00a0<strong>GRAPH OF SINE AND COSINE FOR ANGLES<br \/>\n<\/strong><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and7106.png\" alt=\"\"\/>In the figure below, a circle has been drawn on a Cartesian plane so that its radius, OP, is of length 1unit. Such a circle is called <strong>unit circle.<br \/>\n<\/strong><br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and7107.png\" alt=\"\"\/>The angle \u0472 that OP makes with Ox changes according to the position of P on the circumference of the unit circle. Since P is the point (x,y) and \/OP\/ = 1 unit,<br \/>\n         Sin \u0472 = y\/1     = y<br \/>\n          Cos \u0472 = x\/1   = x<br \/>\nHence the values of x and y give a measure of cos \u0472 and sin \u0472 respectively.<br \/>\nIf the values of \u0472 are taken from the unit circle, they can be used to draw the graph of sin \u0472. This is done by plotting values of y against corresponding values of \u0472 as in the figure below.<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0In the figure above, the vertical dotted lines gives the values of sin \u0472 corresponding to \u0472 = 30<sup>o<\/sup>, 60<sup> o<\/sup>,<br \/>\n90<sup> o<\/sup>,&#8230;&#8230;., 360<sup> o<\/sup>.<br \/>\nTo draw the graph of cos\u0472 , use corresponding values of x and \u0472. This gives another wave-shaped curve, the graph of cos \u0472 as in the figure below.<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0As \u0472 increases beyond 360<sup>o<\/sup>, both curves begin to repeat themselves as in the figures below.<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0Take note of the following:<br \/>\n1)All values of sin \u0472 and cos \u0472 lie between +1 and -1.<br \/>\n2)The sine and cosine curves have the same shapes but different starting points.<br \/>\n3)Each curve is symmetrical about its peak(high point) and trough(low point). This means that for any value of sin \u0472 there are usually two angles between 0<sup> o<\/sup> and 360<sup> o<\/sup>; likewise for cos \u0472. The only exceptions to this are at the quarter turns, where sin\u0472 and cos\u0472 have the values given in the table below<\/p>\n<table>\n<tbody>\n<tr>\n<td>\u00a0<\/td>\n<td>0<sup>o<\/sup><\/td>\n<td>90<sup>o<\/sup><\/td>\n<td>180<sup>o<\/sup><\/td>\n<td>270<sup>o<\/sup><\/td>\n<td>360<sup>o<\/sup><\/td>\n<\/tr>\n<tr>\n<td>Sin\u0472<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<td>0<\/td>\n<td>-1<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>Cos\u0472<\/td>\n<td>1<\/td>\n<td>0<\/td>\n<td>-1<\/td>\n<td>0<\/td>\n<td>1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<strong>Examples<br \/>\n<\/strong>1) Referring to graph on page 194 0f NGM Book 1, a)Find the value of sin 252<sup>o<\/sup>, b)solve the equation   5 sin \u0472 = 4<br \/>\nSolution<br \/>\na)On the \u0472 axis, each small square represents 6. From construction a) on the graph:<br \/>\n        Sin 252<sup>o<\/sup> = -0.95<br \/>\nb)If 5 sin \u0472 = 4<br \/>\n  then sin \u0472 = 4\/5  = 0.8<br \/>\nFrom construction b) on the graph: when sin \u0472 = 0.8, \u0472 = 54<sup>o<\/sup> or 126<sup>o<\/sup><\/p>\n<p>\u00a0<strong>EVALUATION<br \/>\n<\/strong>1)Using the same graph used in the above example, find the values of the following<br \/>\na)sin 24<sup>o<\/sup>    b) sin 294<sup>o<\/sup><br \/>\n\t\t2)Use the same graph  to find the angles whose sines are as follows:<br \/>\na) 0.65     b)-0.15<\/p>\n<p>\u00a0<strong>GENERAL EVALUATION <\/strong><\/p>\n<ol>\n<li>Express the following in terms of sin, cos or tan of an acute angle:\n<\/li>\n<\/ol>\n<ol>\n<li>sin 210<sup>0<\/sup>\n\t\t<\/li>\n<li>tan 240<sup>0<\/sup>\n\t\t<\/li>\n<li>cos(-35<sup>0<\/sup>)\n<\/li>\n<\/ol>\n<ol>\n<li>If cos = -0.6428, find the value of between 0<sup>0<\/sup> and 360<sup>0<\/sup>\n\t\t<\/li>\n<\/ol>\n<p>\u00a0<strong>READING ASSIGNMENT<br \/>\n<\/strong>NGM SS BK 1 pg 114- 123, Ex 11a .<br \/>\nNOS 10 and 25 pg 117 -118<\/p>\n<p>\u00a0<strong>WEEKEND ASSIGNMENT<br \/>\n<\/strong><\/p>\n<ol>\n<li>If Sin A  = 4\/5, what is tan A? A 2\/5 B. 3\/5 C. \u00be\u00a0\u00a0\u00a0\u00a0D. 1 E. 4\/3\n<\/li>\n<li>Use tables to find the value of 8 Cos 77. A. 5.44\u00a0\u00a0\u00a0\u00a0B. 6.48\u00a0\u00a0\u00a0\u00a0 C. 9.12 D 7.57 E. 1.80\n<\/li>\n<li>If cos \u03b8 = sin 33 <sup>o<\/sup>, find tan \u03b8. A. 1.540 B. 2.64 C.0.64 D. 1.16 E. 1.32\n<\/li>\n<li>If the diagonal of a square is 8cm, what is the area of the square? A 16cm<sup>2<\/sup>B. 2cm<sup>2<\/sup> C. 4cm<sup>2<\/sup>D. 20cm<sup>2<\/sup>E. 10cm<sup>2<\/sup>\n\t\t<\/li>\n<li>\n<div>Calculate the angle which the diagonal in question 4 makes with any of the side of the square. A. 65<sup>o<\/sup>B. 45<sup>o<\/sup>C. 35<sup>o<\/sup>D. 25<sup>o<\/sup>E. 75<sup>o<\/sup>\n\t\t\t<\/div>\n<p>\u00a0<br \/>\n\u00a0<strong>THEORY<br \/>\n<\/strong><\/li>\n<li>From a place 400m north of X, a student walks east wards to a place Y which is 800m from X. What is the bearing of X from Y?\n<\/li>\n<li><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1057_Week6and7108.png\" alt=\"\"\/>In the figure below, the right angles and lengths of sides are as shown. Calculate the value of K .\n<\/li>\n<\/ol>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00a0WEEK SIX Review of the first half term&#8217;s work and periodic test WEEK SEVEN TOPIC:&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,190],"tags":[],"class_list":["post-2213","post","type-post","status-publish","format-standard","hentry","category-posts","category-second-term-ss1-general-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2213","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/comments?post=2213"}],"version-history":[{"count":1,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2213\/revisions"}],"predecessor-version":[{"id":2214,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2213\/revisions\/2214"}],"wp:attachment":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/media?parent=2213"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/categories?post=2213"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/tags?post=2213"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}