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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]

Derivatives of Trigonometric Functions

Lesson 3.5

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

Find the derivative.

Find the derivative.

Find the derivative.

Find the derivative.

Find the derivative.

Remember that cos2 x + sin2 x = 1

So sin x = 1 – cos2x

Find the derivative.

- 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

Find the derivative of y.

Find the derivative of y.

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

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

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

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

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