if 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?

Using ur calculator you should get  15 degrees ( Use the sin-1  key.).

Angle complementary to x  is 90-15 = 75 degrees

and as  sin x = cos(90-x)  then cos 75 is also equal 0.2588