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Drill

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

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  1. 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]

  2. Derivatives of Trigonometric Functions Lesson 3.5

  3. Objectives • Students will be able to • use the rules for differentiating the six basic trigonometric functions.

  4. Find the derivative of the sine function.

  5. Find the derivative of the sine function.

  6. Find the derivative of the cosine function.

  7. Find the derivative of the cosine function.

  8. Derivatives of Trigonometric Functions

  9. Example 1 Differentiating with Sine and Cosine Find the derivative.

  10. Example 1 Differentiating with Sine and Cosine Find the derivative.

  11. Example 1 Differentiating with Sine and Cosine Find the derivative.

  12. Example 1 Differentiating with Sine and Cosine Find the derivative.

  13. Example 1 Differentiating with Sine and Cosine Find the derivative. Remember that cos2 x + sin2 x = 1 So sin x = 1 – cos2x

  14. Example 1 Differentiating with Sine and Cosine Find the derivative.

  15. 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

  16. Find the derivative of the tangent function.

  17. Find the derivative of the tangent function.

  18. Derivatives of Trigonometric Functions

  19. Derivatives of Trigonometric Functions

  20. More Examples with Trigonometric Functions Find the derivative of y.

  21. More Examples with Trigonometric Functions Find the derivative of y.

  22. 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

  23. 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

  24. 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

  25. 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

  26. Homework, day #2 • Page 146: 4, 6, 9, 11, 12, 17-20, 22 28, 32

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