Find all values of B in the interval [0°,360°) that satisfy the equation. Use degree measure.3 csc *p - 16 csc?p + 16 = 0The solution set is )(Round to the nearest tenth as needed. Do not include the degree symbol in your answer. Use a comma to separate answers as needed.)

Answered: Find all values of ß in the interval…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.3: Trigonometric Functions Of Real Numbers

Problem 36E

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Find all values of B in the interval [0°,360°) that satisfy the equation. Use degree measure.
3 csc *p - 16 csc?p + 16 = 0
The solution set is )
(Round to the nearest tenth as needed. Do not include the degree symbol in your answer. Use a comma to separate answers as needed.)

Expert Solution

Step 1

$3 c s c^{4} β - 16 c s c^{2} β + 16 = 0 f a c t o r i z e 3 c s c^{4} β - 12 c s c^{2} β - 4 c s c^{2} β + 16 = 0 3 c s c^{2} β (c s c^{2} β - 4) - 4 (c s c^{2} β - 4) = 0 (c s c^{2} β - 4) (3 c s c^{2} β - 4) = 0 c s c^{2} β = 2, \frac{4}{3} o r \sin^{2} β = \frac{1}{2} . \frac{3}{4} t h e r e f o r e \sin β = \pm \frac{1}{\sqrt{2}}, \pm \frac{\sqrt{3}}{2}$

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