Explanation The sign of the trigonometric functions is dependent on the signs of the coordinates of the point. The signs of various trigonometric functions are mentioned in the following figure: Given: s i n θ = 4 5 , where π 2 < θ < π Formula used: s i n 2 θ + c o s 2 θ = 1 Calculation: Given that s i n θ = 4 5 , where π 2 < θ < π Now we know that s i n 2 θ + c o s 2 θ = 1 ( 4 5 ) 2 + c o s 2 θ = 1 c o s 2 θ = < To determine (b) Find the value of s i n 2 θ if s i n θ = 4 5 , where π 2 < θ < π To determine (c) The value of c o s e c θ 2 if s i n θ = 4 5 , where π 2 < θ < π

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.

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Question

Chapter 1, Problem 44CRE

To determine

(a)

The value of tan θ if sin θ = 45, where π2 < θ < π

To determine

(b)

Find the value of sin 2 θ if sin θ = 45, where π2 < θ < π

To determine

(c)

The value of cosec θ2 if sin θ = 45, where π2 < θ < π

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Chapter 1, Problem 43CRE

Chapter 1, Problem 45CRE

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Chapter 1 Solutions

Calculus - Standalone book

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