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 & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 32T

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Question

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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