Explain why sinx degrees= cos(90-x)degrees. include a diagram with your explanation.

Answer 1

construct a right angled triangle, let one non-90° angles be x, then the other is 90-x

recall sinx = opposite/hypotenuse
and cosx = adjacent /hypotenuse

but when we look at the angles x and 90-x, the opposite of one becomes the adjacent of the other
So it should be very easy to see why the relationship is true

or

using the identity
cos(A-B) = cosAcosB + sinAsinB
we have
cos(90-x) = cos90cosx + sin90sinx
= 0(cosx) + 1(sinx)
= sinx