3.5 Derivatives of Trig Functions

Consider the function We could make a graph of the slope: slope Now we connect the dots! The resulting curve is a cosine curve. What function does the red curve look like?

Derivative of y = sin x USING LIMITS:

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

We can find the derivative of tangent x by using the quotient rule. Now use the quotient rule:

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

SAME Rules for Finding Derivatives Simple Power rule Sum and difference rule Constant multiple rule Product rule Quotient rule

Trig Identities Don’t forget these!!!!

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

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

Example 3 Find if.

Find the derivatives

Simple Harmonic Motion A weight 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. Its position at any later time t is s = 5cos. What is its velocity and acceleration at time t? Describe it’s motion. Position : Velocity : Acceleration :

Find the slope at the given point: 1.) at the point (0, 1)

Find the slope at the given point: 1.) at the point (0, 1)

Find the slope at the given point: 1.) at the point (π, -π)

Find the slope at the given point: 1.) at the point

Find the derivative of each: 1.)2.)

Find the derivative of each: 3.)4.)

Find the derivative of each: 5.)6.)

Find the derivative of each: 7.)8.)

Find the derivative of each: 9.)10.)

Find: