I have read a few websites and a book on trigonometric identities and I know that:
cos x = sin 90 - x
cos^2 + sin^2 x = 1
sin x / cos x = tan x

I am not sure how to solve an equation whith z(sin x) and (cos y)
For example sovle the equation:
3(sin 20) = cos(2x)    [degrees]
(find x for 0 <= x <=180)

Thanks

In general, equations like this cannot be solved without invoking the
so-called inverse trigonometric functions. For example, to solve your
example for x:

z*sin(y) = cos(2x)

We could write:

2x = arccos(z*sin(y)), where arccos(a) is the inverse of the cosine function

Thus, we can formally solve it by saying:

x = arccos(z*sin(y))/2

Unfortunately, your example has no solution, since 3*sin(20) is bigger
than one and thus cannot equal cos(2x) for any value of x.