Question

Find all solutions to the equation.
7 sin2x - 14 sin x + 2 = -5

Can someone walk me through this?
The online notes are little help.

Answer 1

You can set it up as \[sinx = x\] then you have \[7x^2-14x+2 = -5\] or you can just use sinx, but this may seem easier to you so you can plug in sinx afterwards for x. You'll have to use difference of squares.

Answer 2

First, add the 5 to both side to get a 0 on the right side.

Answer 3

Yeah.

Answer 4

Then I just solve for x?

Answer 5

Okay thanks. I didn't realize it was that simple.

Answer 6

You can factor out a seven and then factor for the rest.

Answer 7

Yeah, and you'll have to plug sinx back as x to find the solution

Answer 8

So you'd finally come to
7(x+1)(x-1)
then what do you do?