sec n9.4 Determine all of the solutions in the interval 0° < 0 < 360°. (Enter your answers as a comma-separated list.)sin 20 = 2 cos eNeed Help?Read ItWatch It

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Math

Calculus

Determine all of the solutions in the interval 0° se < 360°. (Enter your answers as a comma-separated list.) sin 20 - 2 cos e

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section: Chapter Questions

Problem 25RE

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Concept explainers

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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sec n9.4

Determine all of the solutions in the interval 0° < 0 < 360°. (Enter your answers as a comma-separated list.)
sin 20 = 2 cos e
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Expert Solution

Step 1

given trigonometric equation

$\sin 2 θ = 2 cosθ substract both side by \sin 2 θ \Rightarrow - \sin 2 θ + 2 cosθ = 0 [use the trigonometric fromula : \sin 2 θ = 2 sinθcosθ] \Rightarrow - 2 sinθcosθ + 2 cosθ = 0 \Rightarrow 2 cosθ (- sinθ + 1) = 0 now equate cosθ = 0, 1 - sinθ = 0 cosθ = 0 \Rightarrow θ = \frac{- 3 π}{2}, \frac{- π}{2}, \frac{3 π}{2}, \frac{π}{2}, \frac{5 π}{2} . . . . . . . . . . . . . .$

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