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### Derivatives of Trigonometric Functions

Drill

- Convert 105 degrees to radians
- Convert 5π/9 to radians
- What is the range of the equation y = 2 + 4cos3x?

- 7π/12
- 100 degrees
- [-2, 6]

Lesson 3.5

Objectives

- Students will be able to
- use the rules for differentiating the six basic trigonometric functions.

Example 1 Differentiating with Sine and Cosine

Find the derivative.

Example 1 Differentiating with Sine and Cosine

Find the derivative.

Example 1 Differentiating with Sine and Cosine

Find the derivative.

Example 1 Differentiating with Sine and Cosine

Find the derivative.

Example 1 Differentiating with Sine and Cosine

Find the derivative.

Remember that cos2 x + sin2 x = 1

So sin x = 1 – cos2x

Example 1 Differentiating with Sine and Cosine

Find the derivative.

Homework, day #1

- Page 146: 1-3, 5, 7, 8, 10
- On 13 – 16
- Velocity is the 1st derivative
- Speed is the absolute value of velocity
- Acceleration is the 2nd derivative
- Look at the original function to determine motion

More Examples with Trigonometric Functions

Find the derivative of y.

More Examples with Trigonometric Functions

Find the derivative of y.

Whatta Jerk!

Jerk is the derivative of acceleration. If a body’s position at time t is s(t), the body’s jerk at time t is

Example 2 A Couple of Jerks

Two bodies moving in simple harmonic motion have the following position functions:

s1(t) = 3cos t

s2(t) = 2sin t – cos t

Find the jerks of the bodies at time t.

velocity

acceleration

Example 2 A Couple of Jerks

Two bodies moving in simple harmonic motion have the following position functions:

s1(t) = 3cos t

s2(t) = 2sin t – cos t

Find the jerks of the bodies at time t.

velocity

jerk

acceleration

Example 2 A Couple of Jerks

Two bodies moving in simple harmonic motion have the following position functions:

s1(t) = 3cos t

s2(t) = 2sin t – cos t

Find the jerks of the bodies at time t.

velocity

acceleration

jerk

Homework, day #2

- Page 146: 4, 6, 9, 11, 12, 17-20, 22 28, 32

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