1. Compound Angle Formulae 1. Addition Formulae Example:

2. 2. Formulae Involving Double Angle (2A)

3. Mixed Examples: Substitute form the tan (sin/cos) equation +ve because A is acute Similarly: 3-4-5 triangle !!! A is greater than 45 degrees – hence 2A is greater than 90 degrees.

4. Q.E.D.

6. (A Higher Question) The sine rule From the diagram: The sum of the angles of a triangle=180 As required

8. TRIGONOMETRIC EQUATIONS Double angle formulae (like cos2A or sin2A) often occur in trig equations. We can solve these equations by substituting the expressions derived in the previous sections. sin2A = 2sinAcosAwhen replacing sin2A cos2A = 2cos 2 A – 1 if cosA is also in the equation cos2A = 1 – 2sin 2 Aif sinA is also in the equation when replacing cos2A Use

9. cos2x and sin x, so substitute 1-2sin 2

10. cos 2x and cos x, so substitute 2cos 2 -1 c a s t All S_ Talk C*&p ??

11. 360 o -2 0 2 4 -4 Three problems concerning this graph follow.

12. 360 o -2 0 2 4 -4 The max & min values of asinbx are 3 and -3 resp. The max & min values of sinbx are 1 and -1 resp. f(x) goes through 2 complete cycles from 0 – 360 o The max & min values of csinx are 2 and -2 resp.

13. From the previous problem we now have: Hence, the equation to solve is: Expand sin 2x Divide both sides by 2 Spot the common factor in the terms? Is satisfied by all values of x for which:

14. From the previous problem we have: Hence: