Week 7 and 8 – Jss 3 Second Term Mathematics Notes

WEEK SEVEN
MID TERM EXAMINATION
WEEK 8
THE TRIGONOMETRIC RATIOS
The 3 trigonometric ratios are sine (sin), cosine (cos) and tangent (tan)
Consider the right-angled triangle below

 
 
 
 
 
 Hypotenuse: the longest side is called hypotenuse

1. Tangent of an Angle

   In any right angle triangle tangent =

    Example
   Use the table of tangent to write down the values of the following (a) tan 36^o (b) tan 23.5^o (c) tan 45^o
   

Solution

1. Tan 36^o. look for 36^o under the column headed x tan 36^o = 0.7265
2. Tan 23.5^o look for 23⁰ under the column headed x. then move across until under the column headed 0.5^o to find 0.4348 tan 23.5^o = 0.4348
3. Tan 45⁰ = 1

Exercise: in ABC, Ĉ = 90, B = 28^o and CA = 12cm. Find BC. Give your answer to 2.s.f
SINE AND COSINE OF AN ANGLE
Sine =, Cosine =
The three ratios can be summarized in the word SOH CAH TOA
Sin =,          Cos,         tan
Example: Use tables of sine and cosine to find (a) Sin 46.65^o (b) cos 15.94^{o =} 0.9615
Solution

1. Sin 46.65^o = 0.7266 (b) cos 15.94^o

Exercise: Find the size of an in the triangles below

1.                         (b)