1. Derivatives of Trig Functions Objective: Memorize the derivatives of the six trig functions

2. Derivative of the sin(x) The derivative of the sinx is:

3. Derivative of the sin(x) The derivative of the sinx is: Lets look at the two graphs together.

4. Derivative of the cos(x) The derivative of the cosx is:

5. Derivative of the cos(x) The derivative of the cosx is: Lets look at the two graphs together.

6. Derivatives of trig functions The derivatives of all six trig functions:

7. Trig Identities

8. Example 1 Find if

9. Example 1 Find if We need to use the product rule to solve.

10. Example 2 Find if

11. Example 2 Find if We need to use the quotient rule to solve.

12. Example 2 Find if We need to use the quotient rule to solve.

13. Example 3 Find if.

14. Example 3 Find if.

15. Example 3 Find if.

16. Example 3 Find if.

17. Example 4 On a sunny day, a 50-ft flagpole casts a shadow that changes with the angle of elevation of the Sun. Let s be the length of the shadow and the angle of elevation of the Sun. Find the rate at which the shadow is changing with respect to when.

18. Example 4 On a sunny day, a 50-ft flagpole casts a shadow that changes with the angle of elevation of the Sun. Let s be the length of the shadow and the angle of elevation of the Sun. Find the rate at which the shadow is changing with respect to when. The variables s and are related by or.

19. Example 4 We are looking for the rate of change of s with respect to. In other words, we are looking to solve for. In this example, is the independent var.

20. Example 4 We are looking for the rate of change of s with respect to. In other words, we are looking to solve for. In this example, is the independent var.

21. Example 4 We are looking for the rate of change of s with respect to. In other words, we are looking to solve for. In this example, is the independent var.

22. Class work Section 2.5 Page 172 2-16 even

23. Homework Section 2.5 Page 172 1-27 odd 31