Question
Asked Nov 21, 2019
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Solve the equation (x in radians and θ in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth.

2 sin2 x + sin x = 1

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Expert Answer

Step 1

Given,

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2 sin2 x sin x = 1 2 sin2 xsin x - 1 0 2 sin2 x2sin x - sin x -1 = 0 2 sin x (sin x + 1) -1( sin x 1) 0 (2sin x 1) sin x 1) 0 Either 2sin x - 1 = 0 or sin x + 1 = 0 sin x 1 sin x

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Step 2

Further calcu...

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Solving for sin x sin(30°), sin(150°) sin x = x = 30°,150 x = 30° +360°n, 150° 360°n (general solution) 5п 2n 6 TT And in radians x = 27n 6 x= 0.5236 +27tn, 2.6180 2n Solving for sin x = -1 sin x sin(270) x 270° 270° + 360°n x Зп +2пп 2 And in radians x = = 4.7124 2tn

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Tagged in

Math

Trigonometry

Trigonometric Ratios