SOLUTION: Use inverse functions where needed to find all solutions of the equation in the interval [0, 2 pi). (Enter your answers as a comma-separated list.) 2 sin^2 x + 9 cos x = 6 X=??

Algebra ->  Trigonometry-basics -> SOLUTION: Use inverse functions where needed to find all solutions of the equation in the interval [0, 2 pi). (Enter your answers as a comma-separated list.) 2 sin^2 x + 9 cos x = 6 X=??      Log On


   

Question 911313: Use inverse functions where needed to find all solutions of the equation in the interval [0, 2 pi). (Enter your answers as a comma-separated list.)
2 sin^2 x + 9 cos x = 6
X=????
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Use inverse functions where needed to find all solutions of the equation in the interval [0, 2 pi). (Enter your answers as a comma-separated list.)
2 sin^2 x + 9 cos x = 6
2sin%5E2%28x%29%2B9cos%28x%29=6
2%281-cos%5E2%28x%29%29%2B9cos%28x%29=6
2-2cos^2x+9cosx=6
2cos^2x-9cosx+4=0
(2cosx-1)(cosx-4)=0
cosx=4(reject)(-1 ≤ cosx ≤ 1
or
cosx=1/2
x=π/3, 5π/3 (in quadrants I and IV where cos>0)