BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 3.4, Problem 91E
To determine

Explain the proof of the given relation using chain rule.

Expert Solution

Explanation of Solution

Given:

The given relationis ddθ(sinθ)=π180cosθ , where θ is measured in degrees.

Calculation:

  ddθ(sinθ)=π180cosθ

From L.H.S

  ddθ(sinθ)

  θ is measured in degrees.

  180°=πradiansθ°=π180°θ°=πθ180radians

  ddθ(sinθ)=ddθ(sinπθ180)

Apply chain rule.

  df(a)dx=dfdadadx

Let f=sin(a),a=πθ180

  ddθ(sinθ)=dda(sina)ddθ(πθ180)

Use derivative rule.

  ddx(sinx)=cosxandddx(xn)=nxn1 .

  ddθ(sinθ)=cosaπ180(1)ddθ(sinθ)=π180cosa

Substitute the value of a=πθ180 .

  ddθ(sinθ)=π180cos(πθ180)ddθ(sinθ)=π180cos(θ°)=R.H.S

Hence ddθ(sinθ)=π180cos(θ°) proved.

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