1. Derivatives of Trig Functions
AP Calculus
Mrs. Mongold

2. Consider the function
slope
We could make a graph of the slope:
Now we connect the dots!
The resulting curve is a cosine curve.

3. We can do the same thing for
slope
The resulting curve is a sine curve that has been reflected about the x-axis.

4. We can find the derivative of tangent x by using the quotient rule.

5. Derivatives of the remaining trig functions can be determined the same way.

6. Example
A wight hanging from a spring is stretched 5 units beyond its rest position (s=0) and released at time t=0 to bob up and down. It’s position at any later time t is s=5cost
What are the velocity and acceleration? Describe its motion.

7. Jerk
The derivative of acceleration is jerk. If a body’s position at time t is s(t) the body’s jerk at time t is
When a ride in a car or bus is jerky, it is not that the accelerations are large but the changes in acceleration are abrupt

8. Example: A couple of jerks
A) the jerk caused by the constant acceleration of gravity (g = -32 ft/sec2) is zero.
This is why we don’t get motion sickness when we are sitting around doing nothing
B) The jerk of a simple harmonic motion from example 1 is what?

9. Example
Find equations for the lines that are tangent and normal to the graph of
at x = 2.

10. Example
Find y’’ if y = secx

11. Homework Blue and Red Book
Page 140/1-10, 12-14, 17, 20-22, 26-27