13. @Solve for x : cos (2 sin ' x) = 5 x>0
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Step-by-step explanation:
Use the double angle formula for cosine involving just the sine!
3(1 - 2sin2x) + sin x = -2
3 - 6sin2x + sin x = -2
Set one side equal to zero!
0 = 6sin2x - sin x - 5
Factor!
0 = (6sin x + 5)(sin x - 1)
sin x = -5/6 or sin x = 1
sin x = 1 means x = 90o
The reference angle for the first solution is x = 56.4o Since we need the number negative, the answers are in the III and IV quadrants.
x = 180 + 56.4 = 236.4o or x = 360 - 56.4 = 303.6o
x = 90o, 236.4o, 303.6o
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