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3.5 – Derivatives of Trig Functions

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Presentation on theme: "3.5 – Derivatives of Trig Functions"— Presentation transcript:

1 3.5 – Derivatives of Trig Functions
Ch. 3 – Derivatives 3.5 – Derivatives of Trig Functions

2 Derivatives you absolutely must know:
Derivatives that you probably should memorize: Also, know that sin2x + cos2x = 1 Ex: Find the derivative of f(x)=x3sinx. Use product rule!

3 Ex: Find the derivative of .
Use quotient rule! Trig Identity!

4 Ex: Find the equation of a line tangent to f(x) at x=π/4.
We need f(x) at x=π/4… Now write the tangent line equation…

5 Ex: A weight on a spring is stretched 5 inches beyond its rest position and then released at time t=0 seconds. Its position at time t follows the equation s(t)=5cost. Answer the following questions using a calculator: What is the displacement of the weight after 1 s? What is the average velocity over the first 4 s? Find the velocity at 1 s. What is the fastest speed the weight reaches? We need a maximum or minimum velocity, so find when acceleration is zero!

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