1. Derivatives of Trig Functions
Section 3.3

2. Derivatives of Sine and Cosine

3. Derivative Rules
𝑑 𝑑𝑥 sin 𝑥 = cos 𝑥
𝑑 𝑑𝑥 cos 𝑥 =− sin 𝑥

4. Come up with the following rules…
𝑑 𝑑𝑥 tan 𝑥 =
𝑑 𝑑𝑥 csc 𝑥 =
𝑑 𝑑𝑥 sec 𝑥 =

5. Find the derivative… 𝑦=2 sin 𝑥 −4 cos 𝑥 + tan 𝑥 𝑦= 𝑥 3 sec 𝑥
𝑦=𝑥 𝑒 𝑥 cot 𝑥

6. Application
Find an equation of the tangent line to the curve 𝑦=3𝑥+6 cos 𝑥 at the point where 𝑥= 𝜋 3 . Graph the curve and the tangent line on the same coordinate plane.

7. Application
For what values of 𝑥 does the graph of 𝑓 have a horizontal tangent?
𝑓 𝑥 = 𝑒 𝑥 cos 𝑥

8. Application
A mass on a spring vibrates horizontally on a smooth level surface. Its equation of motion is 𝑥 𝑡 = 8 sin 𝑡 , where 𝑡 is in seconds and 𝑥 is in centimeters.
Find the velocity and the acceleration at time 𝑡.
Find the position, velocity, and acceleration of the mass at time 𝑡= 2𝜋 3 . In what direction is it moving at that time?