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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
Drill
• 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

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.

Remember that cos2 x + sin2 x = 1

So sin x = 1 – cos2x

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
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