Question

What is the y-value of sin(x) when x= -180°?

Answer 1

In trigonometry, we start from the point (1,0), so this is the 0-degree point. Then, we start rotating counter clockwise along the unit circle.

Note that rotating 180 or -180 degrees is actually the same, because you travel half the circumference clockwise or counter clockwise. In both cases, you start from the rightmost point of the circle, (1,0), and arrive at the leftmost point, (-1,0).

Now, for every point (x,y) on the unit circle, given by a certain angle $\alpha$, we have

$\cos(\alpha)=x,\quad \sin(\alpha)=y$

So, in this case, the angle of -180 is associated with the point (-1,0), and thus we have

$\sin(-180)=0$