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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]


Derivatives of trigonometric functions

Derivatives of Trigonometric Functions

Lesson 3.5


Objectives

Objectives

  • Students will be able to

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


Find the derivative of the sine function

Find the derivative of the sine function.


Find the derivative of the sine function1

Find the derivative of the sine function.


Find the derivative of the cosine function

Find the derivative of the cosine function.


Find the derivative of the cosine function1

Find the derivative of the cosine function.


Derivatives of trigonometric functions1

Derivatives of Trigonometric Functions


Example 1 differentiating with sine and cosine

Example 1 Differentiating with Sine and Cosine

Find the derivative.


Example 1 differentiating with sine and cosine1

Example 1 Differentiating with Sine and Cosine

Find the derivative.


Example 1 differentiating with sine and cosine2

Example 1 Differentiating with Sine and Cosine

Find the derivative.


Example 1 differentiating with sine and cosine3

Example 1 Differentiating with Sine and Cosine

Find the derivative.


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


Example 1 differentiating with sine and cosine5

Example 1 Differentiating with Sine and Cosine

Find the derivative.


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


Find the derivative of the tangent function

Find the derivative of the tangent function.


Find the derivative of the tangent function1

Find the derivative of the tangent function.


Derivatives of trigonometric functions2

Derivatives of Trigonometric Functions


Derivatives of trigonometric functions3

Derivatives of Trigonometric Functions


More examples with trigonometric functions

More Examples with Trigonometric Functions

Find the derivative of y.


More examples with trigonometric functions1

More Examples with Trigonometric Functions

Find the derivative of y.


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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