Trigonometric Equation 3.2sin²xCOs x - 1 =0 Find all solutions in the interval from 0 <*0 < 27.

Name: Trigonometric Equation 3.2sin²xCOs x - 1 =0 Find all solutions in the
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Description: Trigonometric Equation 3.2sin²xCOs x - 1 =0 Find all solutions in the interval from 0 <*0 < 27.

Answered: 2 sin? x- cos x – 1= 0

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter6: Fractions

Section6.1: Simplifying Fractions

Problem 38WE

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Trigonometric Equation

Find all solutions in the interval from 0 <*0 < 27.

Expert Solution

Step 1

Given :

$2 \sin^{2} x - \cos x - 1 = 0$

Step 2 : Simplification

$2 \sin^{2} x - \cos x - 1 = 0$

Using $\sin^{2} θ + \cos^{2} θ = 1$ ,

$\begin{array}{rcl} 2 (1 - \cos^{2} x) - \cos x - 1 & = & 0 \\ 2 - 2 \cos^{2} x - \cos x - 1 & = & 0 \\ 2 \cos^{2} x + \cos x - 1 & = & 0 \end{array}$

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