Aus Online Mathematik Brückenkurs 1

A useful technique for calculating the value of a trigonometric function for angles that don't lie between \displaystyle 0 and \displaystyle {\pi }/{2}\; is to use the unit circle. If we draw a line which starts at the origin and makes a certain angle relative to the positive part of the \displaystyle x -axis, we can see that the cosine of that angle is the \displaystyle x -coordinate of the point of intersection between the line and the unit circle. In the same way, the sine of the angle is the \displaystyle y -coordinate of the intersection point.

In this case, we see immediately that \displaystyle \text{sin}\left( -\frac{\pi }{2} \right)\text{ }=\text{ }-\text{1}.