SOLUTION: 4 sin squared x + 1=

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Question 252482: 4 sin squared x + 1= - 4 sin x
Found 2 solutions by stanbon, drk:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
4 sin squared x + 1= - 4 sin x
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4sin^2(x) + 1 = -4sin(x)
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4sin^2(x) + 4sin(x) + 1 = 0
Factor:
(2sin(x)+1)^2 = 0
---
2sin(x)+1 = 0
2sin(x) = -1
sin(x) = -1/2
x = 150 degrees of x = 210 degrees.
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Cheers,
Stan H.

Answer by drk(1908) (Show Source):
You can put this solution on YOUR website!
Here is the original equation:
4*sin^2(x) + 1= -4*sin(x)
First we want to set it = 0.
4*sin^2(x) + 4*sin(x) +1 = 0
Let sin(x) = U; this is a generic dummy variable to make the problem easier to solve.

Now we factor as normal to get

Solving for u, we get

Remember we used U as a dummy variable. We have to resubstitute sin(X) back in as

We want to know what X values may the sin -1/2. The sign will be -1/2 at X = 150 degrees and 210 degrees. In radians, X = 5pi/6 and 7pi/6.

SOLUTION: 4 sin squared x + 1= - 4 sin x