### FORM FOUR MATHEMATICS STUDY NOTES **TOPIC 5: TRIGONOMETRY**

**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.

From the figure above the distance d is given by

In general

Example 15

1. Withoutusing tables find the value of each of the following:

- Sin 75°
- Cos105

*Solution:*Example 16

Find:

- Sin150°
- Cos 15°

Exercise 4

1. Withoutusing tables, find:

- Sin15°
- Cos 120°

2. FindSin 225° from (180°+45°)

3. <!–[endif]–>Verify that

- Sin90° = 1 by using the fact that 90°=45°+45°
- Cos90°=0 by using the fact that 90°=30°+60°

4. <!–[endif]–>Express each of the following in terms of sine, cosine and tangent of acute angles.

- Sin107°
- Cos300°

5. <!–[endif]–>By using the formula for Sin (A-B), show that Sin (90°-C)=Cos C