These coordinates do not create a right triangle

Question

I'm supposed to find out what the angle u is. I can't do arcsin of u because it isn't a right triangle (according to this site). I can't use the sine or cosine rules either because none of the angles are known. How do I find this angle?

Answer 1

The coordinates of a point in a cricle with center $(c_1,c_2)$ and radius $r$ are $(c_1+r\cdot \cos(\alpha),c_2+r\cdot \sin(\alpha))$ with $\alpha$ being the angle between the horizontal axis and the line joining the center of the circumference and the point.

Characterize this to your problem and with the fundamental laws of the trigonometry find the angle.

Answer 2

Project point $P$ on the horizontal axis. Then you have a right angle triangle. The side $a$ in your calculator is the $0.722$ value, the side $b$ is $0.692$. The calculated $c$ value is very close to $1$ (within numerical precision), which is the radius of the unit circle (as expected).