Derivatives of Trigonometric Functions Section 3.3

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

Example 2, differentiate

Example 3, differentiate

Example 3, differentiate

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.

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.

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.

Example 5, nth derivative Therefore,

Example 6, Find limit

Example 7, find the limit

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