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Trigonometry | 7th Edition | ISBN: 9781111826857 | Authors: Charles P. McKeague ISBN: 9781111826857 186

Solution for problem Problem 2 Chapter 5.1

Trigonometry | 7th Edition

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Trigonometry | 7th Edition | ISBN: 9781111826857 | Authors: Charles P. McKeague

Trigonometry | 7th Edition

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Problem Problem 2

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MTH 132 ­ Lecture 9 ­ Trigonometric Derivatives Sine and Cosine addition ● sin(a+b) = sin(a)cos(b)+cos(a)sin(b) ● cos(a+b) = cos(a)cos(b)­sin(a)sin(b) Derivative of Sine ● sin(x)’ = cos(x) Sine Proof ● [ sin(x+h) ­ sin(x) ] / h ● [ Sin(x)cos(h) + cos(x)sin(h) ­ sin(x) ] / h ● Cos(x) * sin(h)/h ​ sin(x) * (cos(h) ­ 1)/h ○ [cos(h) ­1]/h always = 0 ● Simplify to get cos x as h approaches 0. Cosine Derivative ● cos(x)’ = ­sinx Cosine Proof ● f(x) = cosx ● f’(x) = limit h approaches 0 [ f(x+h) ­ f(x) ]/ h ● cos(x+h) ­ cos(x) = cos(x)cos(h) ­ sin(x)sin(h) ­ cos(x) ● cos(x)*[cos(h)­1]/h ­ sinx*sin(h)/h ● sin^2x+cos^2x = 1 ● (sin^2x+cos^2x )’= 1’ ● (sinx*sinx)’ + (cosx*

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Chapter 5.1, Problem Problem 2 is Solved
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Textbook: Trigonometry
Edition: 7
Author: Charles P. McKeague
ISBN: 9781111826857

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