Question

If two angles are supplementary, then their sines are equal. Explain why. What about the cosines of supplementary angles? If you are not sure, calculate some examples.

Answer 1

Have you learned the expansion formulas for
sin(A-B) and cos(A-B)

that is,
sin(A-B) = sinAcosB - cosAsinB

I will have to know to determine which approach to show you

Answer 2

yes I have.

Answer 3

then take
sin(180-x) , where we know x and 180-x are supplementary

= sin180cosx - cos180sinx
= 0 - (-1)sinx
= sinx

so sinx = sin(180-x)

now for the second
cos(180-x)
= cos180cosx + sin180sinx
= (-1)cosx + 0
= - cosx

and cos(180-x) = -cosx