SOLUTION: Find all solutions to the equation. 7 sin^(2)x - 14 sin x + 2 = -5

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Question 1113683: Find all solutions to the equation.
7 sin^(2)x - 14 sin x + 2 = -5
Found 2 solutions by KMST, Edwin McCravy:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
7+sin%5E2%28x%29+-+14+sin%28x%29+%2B+2+=+-5
7+sin%5E2%28x%29+-+14+sin%28x%29+%2B+7+=+0
7%28sin%5E2%28x%29-+2+sin%28x%29+%2B+1%29=+0
7%28sin%28x%29-1%29%5E2=+0
%28sin%28x%29-1%29%5E2=+0
sin%28x%29-1=+0
sin%28x%29=1
That happens only for pi%2F2 and all co-terminal angles.
So you could say that highlight%28x=pi%2F2%2B2k%2Api%29 for all k integers.

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
7sin²x - 14sinx + 2 = -5

Get 0 on the right by adding 5 to both sides:

7sin²x - 14sinx + 7 = 0

Since every term is divisible by 7, we divide through by 7:

sin²x - 2sinx + 1 = 0

Factor as a trinomial:

(sinx-1)(sinx-1) = 0

(sinx-1)² = 0

sinx-1 = 0

sinx = 1

x = p/2 + 2p∙n

Edwin