Drill
Sponsored Links
This presentation is the property of its rightful owner.
1 / 28

Drill PowerPoint PPT Presentation


  • 100 Views
  • Uploaded on
  • Presentation posted in: General

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

Download Presentation

Drill

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


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


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 cosine function.


Find the derivative of the cosine function.


Derivatives of Trigonometric Functions


Example 1 Differentiating with Sine and Cosine

Find the derivative.


Example 1 Differentiating with Sine and Cosine

Find the derivative.


Example 1 Differentiating with Sine and Cosine

Find the derivative.


Example 1 Differentiating with Sine and Cosine

Find the derivative.


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 Cosine

Find the derivative.


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.


Derivatives of Trigonometric Functions


Derivatives of Trigonometric Functions


More Examples with Trigonometric Functions

Find the derivative of y.


More Examples with Trigonometric Functions

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


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


  • Login