Got so far in a math problem but a little stumped for the solution...?

Question

I've doe a lot of twists and turns doing a statics problem and it all boils down to this:

-66sin(Theta) + 22cos(Theta) = 160.751

I know the answer is 28.9 degrees and the equation comes out to that, but I'm not sure how to solve it from here.

Please help.

Answer 1

Just use the identity sin^2+cos^2=1.

sin(theta)=sqrt(1-cos^2(theta))

Let cos(theta)=x and you end up with a quadratic equation which you can solve for x.  Then solve for theta.