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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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Drill
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]



Objectives
Objectives

  • Students will be able to

    • use the rules for differentiating the six basic trigonometric functions.











Example 1 differentiating with sine and cosine4
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
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
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
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 jerks1
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 jerks2
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
Homework, day #2

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


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