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:
Graph the sin function and try to draw the graph of the derivative. What does this graph look like?

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

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

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

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

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

8. Trig Identities

9. Trig Identities

10. Trig Identities

11. Example 1
Find if

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

13. Example 2
Find if

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

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

16. Example 3
Find if

17. Example 3
Find if

18. Example 3
Find if

19. Example 3
Find if

20. 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 Express your answer in degrees.

21. 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

22. 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.

23. 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.

24. 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.

25. 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.

26. 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.
Both answers can’t be right. Which one is?

27. 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.

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

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