I am asked to show that |sin(x)|=|AC|, where x=theta and -pi/2< x< pi/2 and AC corresponds to the length of the vertical line that falls from the point (cosx,sinx) on the unit circle to the horizontal x-axis. I am also asked to show both cases, positive and negative, for x=theta.
The positive case, sin(x)=AC, is trivial to show as sin(x)=y/r. That simplifies to just y=AC, so sin(x)=AC and, making the substitution, AC=AC.
The negative case however, trips me up a bit. I chose to tack the negative sign on the left side of the equation to get -sin(x)=AC, but -sin(x)=-y/r. Thus -sin(x)=-y=-AC. -AC does not equal AC. Could someone show me step by step how to do the negative case please?