1. Derivatives of Trigonometric Functions
Section 3.3

3. Example 1, differentiate
Differentiate y = x2 sin x.
Solution:

4. Example 2, differentiate

6. Example 3, differentiate

7. Example 3, differentiate

8. Derivatives of Trigonometric Functions
Trigonometric functions are often used in modeling real-world phenomena. In particular, vibrations, waves, elastic motions, and other quantities that vary in a periodic manner can be described using trigonometric functions. In the following example we discuss an instance of simple harmonic motion.

9. Example 4, velocity and acceleration
An object at the end of a vertical spring is stretched 4 cm beyond its rest position and released at time t = 0.
Its position at time t is
s = f (t) = 4 cos t
Find the velocity and acceleration
at time t.

10. Example 4 – Solution The velocity and acceleration
The object oscillates from the lowest point (s = 4 cm) to the highest point (s = –4 cm). The period of the oscillation is 2, the period of cos t.

11. Example 5, nth derivative
Therefore,

12. Example 6, Find limit

13. Example 7, find the limit

14. 3.3 Derivatives of Trigonometric Functions
Summarize Notes
Read section 3.3
Homework
Pg.197 #3,5,9,15,21,23,25,29,31,33,35,39,45,49