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]

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Presentation transcript:

Drill Convert 105 degrees to radians Convert 5π/9 to radians What is the range of the equation y = 2 + 4cos3x? 7π/ 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 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 cos 2 x + sin 2 x = 1 So sin x = 1 – cos 2 x

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 1 st derivative  Speed is the absolute value of velocity  Acceleration is the 2 nd derivative  Look at the original function to determine motion

Find the derivative of the tangent function.

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: s 1 (t) = 3cos t s 2 (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: s 1 (t) = 3cos t s 2 (t) = 2sin t – cos t Find the jerks of the bodies at time t. velocity acceleration jerk

Example 2 A Couple of Jerks Two bodies moving in simple harmonic motion have the following position functions: s 1 (t) = 3cos t s 2 (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