Question

f sinx is approximately 0.2588, what is the measurement of x to the nearest degree? Approximately, what is the cosine of the angle that is complementary to x?

Answer 1

There are buttons on all scientific calculators for inverse trig functions.

Usually denoted as "arcsin, arccos" or with a little -1 inverse sign like this:
 $sin^{-1} (0.2588) = 14.99$

You put in the measurement and it gives back the angle. I

angle x = 15°

complimentary angles add up to 90° so the angle that's complimentary is 90-15 = 75°