Pre calculus proof

Question

How can you prove that the sine of an angle is equivalent to the sine of its supplement ?

Answer 1

The answer depends on what you know (i.e. take as given), what you consider proof.and how you have defined the sin function.

The simplest way to see it is to draw a picture.

The sine is positive is quadrants I and II and negative is quadrant III and IV.

The co-ordinates of points in the quadrants shows what you wish to prove.

Another way if you have the addition formulae, then sin(180-x)=sin x.