You can put this solution on YOUR website! sin (x-20) is the sine of the difference of two angles.
sin (a-b)= sin(a)cos(b) – cos(a)sin(b)
[sin x * cos (20)] - [cos x * sin (20)] = cos x
cos 20=0.940
sin 20 =0.342
0.940* sin x - 0.342 cos x = cos x
Add 0.342 cos x to both sides
0.940 sin x=1.342 cos x
divide by 0.940
sin x= 1.428 cos x
square both sides.
sin^2 x=2.038 cos^2 x
sin ^2 x=1-cos ^2 x ; This comes from the fact that sin^2 + cos^2= 1
1-cos^2 x = 2.038 cos^2 x
1= 3.038 cos ^2 x
Divide by 3.038
0.329= cos^2 x
Take the square root:
0.574= cos x
Take the arc cos, and x=54.99 deg.
Go back to the original problem.
sin (x-20)=cos x ; This is sin (34.99)= 0.574 (or it should!). And within rounding error, it does.
