Find all solutions to the equation. 7 sin2x - 14 sin x + 2 = -5 If yall can help me for Pre-Calc, that would be great. -Thanks.

Question

asked Sep 27, 2021 96.3k views

1 Answer

Frenchie · Answer 1 · 2021-10-01T02:03:24+0000

If the equation is

$7\sin^2x-14\sin x+2=-5$

then rewrite the equation as

$7\sin^2x-14\sin x+7=0$

Divide boths sides by 7:

$\sin^2x-2\sin x+1=0$

Since
x^2-2x+1=(x-1)^2 , we can factorize this as

$(\sin x-1)^2=0$

Now solve for x :

$\sin x-1=0$

$\sin x=1$

$\implies\boxed{x=\frac\pi2+2n\pi}$

where n is any integer.

If you meant sin(2x) instead, I'm not sure there's a simple way to get a solution...