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# 3.5notestouse - Jerk A sudden change in acceleration is...

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Calculus Section 3.5 Page25 3.5 Derivatives of Trigonometric Functions Derivative of the Sine Function Sketch the y = sin x Sketch the graph of the derivative of y = sin x on the grid below. What do you notice? Now sketch the derivative of the cosine function. What do you notice? Derivative formulas for sine and cosine: π 2 π 2 3 π 2 3 π 2 π −π 2 π 2 π 2 –2 π 2 π 2 3 π 2 3 π 2 π −π 2 π 2 π 2 –2 π 2 π 2 3 π 2 3 π 2 π −π 2 π 2 π 2 –2

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Calculus Section 3.5 Page 26 d dx sin x ( ) = d dx cos x ( ) = Example 1 Revisiting the Differentiation Rules Find the derivative of a) y = 2 + 3sin x cos x b) y = x 2 sin x c) y = x 1 + cos x d) y = cos x 1 sin x Simple Harmonic Motion Example 2 The Motion of a Weight on a Spring A weight hanging from a spring is stretched 5 units beyond its rest position (s = 0) and released at time t = 0 to bob up and down. Its position at any later time t is: s = 5cos t
Calculus Section 3.5 Page27 What is its velocity and acceleration at time t? Describe its motion. 5 Position at t = 0 0 Rest postiion –5 Definition:

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Unformatted text preview: Jerk A sudden change in acceleration is called a “jerk”. Therefore, a 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 j t ( )= da dt = d 3 s dt 3 Example 3 A Couple of Jerks a) Determine the jerk caused by the constant acceleration of gravity. b) Determine the jerk of the simple harmonic motion in Example 2. Derivatives of Other Basic Trigonometric Functions d dx tan x ( ) = d dx cot x ( ) = d dx sec x ( ) = d dx csc x ( )= Proof: Calculus Section 3.5 Page 28 Example 4 Finding Tangent and ,ormal Lines Find the equations for the lines that are tangent and normal to the graph of f x ( ) = tan x x at x = 2. Support graphically. Example 5 Two Derivatives a) Find ′ y if y = 5 sin x b) Find ′ ′ y if y = sec x Assignment II–5 Page 140 – 141 #1 – 10 all± 11 – 23 odd± 26± 27...
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3.5notestouse - Jerk A sudden change in acceleration is...

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