1. Differentiate:What rule are you using?

2. Aims: To learn results of trig differentials for cos x, sin x & tan x. To be able to solve trig differentials that require the chain, product and quotient rules To be able to reverse this process in order to integrate definite and indefinite expressions. Trigonometry Lesson 5 (Differentiation & Integration)

3. The derivative of sin x

4. By plotting the gradient function of y = sin x, we deduce that Functions of the form k sin f ( x ) can be differentiated using the chain rule. Differentiate y = 2 sin 3 x with respect to x. So if y = 2 sin u where u = 3 x Using the chain rule: In general using the chain rule,

5. The derivative of cos x

6. By plotting the gradient function of y = cos x, we deduce that Differentiate y = 3 cos (x 3 + 4) with respect to x. And similarly to the differentiation of sine, it can be shown using the chain rule,

7. Differentiate these!

8. Try these on w/b’s

9. The derivative of cos x Find given that y = – x 2 cos x. Let u = and v = So Using the product rule: We can also now differentiate products and quotients which contain trig functions.

10. The derivative of tan x We can differentiate y = tan x by writing it as Then we apply the quotient rule with u = sin x and v = cos x :

11. Derivatives & Integrals of trigonometric functions These are the differential we have seen: As integration is the reverse of differentiation it follows that: In A2 you will be only asked to integrate sine and cosine functions. It can also be shown using the reverse chain rule that when dealing with the cos and sin of linear functions:

12. Trig Integration Find Complete wheel puzzle Exercise F pg 101 qu 1, 3, 5, 7. Exercise G pg 104 qu 1 c, f, e. 2 and 3. Then Exercise A pg 108 qu 2, 3b, 4b,d,f and 5b, c, f

13. (b) Person A

14. Person B