SOLUTION: What are the possible values of x domain: [0,2pi). 4sin^3(x) + 2sin^2(x) = 2sin(x) + 1 So far I've: set equal to zero: 4sin^3(x) + 2sin^2(x) + 2sin(x) + 1 = 0

Question 381159: What are the possible values of x domain: [0,2pi).
4sin^3(x) + 2sin^2(x) = 2sin(x) + 1
So far I've:
set equal to zero:
4sin^3(x) + 2sin^2(x) + 2sin(x) + 1 = 0
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
First of all when you set everything equal to zero you should obtain

Let a = sin x. The equation then becomes

This is equivalent to . We can factor to obtain

Solving, we obtain a = -1/2, sqrt(2)/2, and -sqrt(2)/2. All of these values are between -1 and 1, so we can find sin^-1 of each of these angles to find all values for x:
or

or

or
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