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# Drill - PowerPoint PPT Presentation

Drill. Convert 105 degrees to radians Convert 5 π /9 to radians What is the range of the equation y = 2 + 4cos3x?. 7 π /12 100 degrees [-2, 6]. Derivatives of Trigonometric Functions. Lesson 3.5. Objectives. Students will be able to

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Presentation Transcript

• Convert 105 degrees 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.

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

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