TOPIC 5: TRIGONOMETRY ~ MATHEMATICS FORM 4
Trigonometric Ratios
The Compound of Angle Formulae or Sine, Cosine and Tangent in Solving Trigonometric Problems
Apply the compound of angle formulae or sine, cosine and tangent in solving trigonometric problems
The aim is to express Sin (α±β) and Cos (α±β) in terms of Sinα, Sinβ, Cosαand Cosβ
Consider the following diagram:

From the figure above <BAD=αand <ABC=βthus<BCD=α+β
From ΔBCD

For
Cos(α±β) Consider the following unit circle with points P and Q on it
such that OP,makes angleα with positive x-axis and OQ makes angle βwith
positive x-axes.
Cos(α±β) Consider the following unit circle with points P and Q on it
such that OP,makes angleα with positive x-axis and OQ makes angle βwith
positive x-axes.

From the figure above the distance d is given by


In general

Example 16
Find:
- Sin150°
- Cos 15°

Exercise 4: TRIGONOMETRY
1. Withoutusing tables, find:
- Sin15°
- Cos 120°
2. FindSin 225° from (180°+45°)
3. Verify that
- Sin90° = 1 by using the fact that 90°=45°+45°
- Cos90°=0 by using the fact that 90°=30°+60°
4. Express each of the following in terms of sine, cosine and tangent of acute angles.
- Sin107°
- Cos300°
5. By using the formula for Sin (A-B), show that Sin (90°-C)=Cos C