Question

Find all solutions to the equation.

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

Answer 1

Start by moving the -5 over to the other side. This sets the equation equal to zero and in the proper form to factor. We have\[7\sin ^{2}x-14sinx+7=0\]dNow if you are familiar with the u substitution, that would be good here. Doing that substitution gives us that u = sin(x) and u^2=sin^2(x). So, in u sub format\[7u ^{2}-14u+7=0\]And of course you can take a 7 out of that to simplify it even further. \[7(u ^{2}-2u+1)=0\]Now factor. This splits up nicely into 7(u-1)(u-1)=0. 7 cannot equal 0, so forget that, toss it out with the trash. We have the quantity of two (u - 1), so we only need to solve one of them. u - 1 = 0 leads to u = 1. Now fill in the sin(x) for u.\[sinx=1\]Your job is to find where the sin of x is 1. There is only one place where the sin(x) = 1, and that's at 90 degrees, or pi/2. Check out this great unit circle! Learn how to use it and use it often! Any other questions, just ask!

Answer 2

thank you