Rotating point by angle

Question

Let $X = (c, 0)$. If I will rotate $X$ by, say, angle $\alpha = \frac{\pi}{4}$, how can I determine position of new angle?

Will it just be $X' = (c + \cos\alpha, \sin\alpha)$?

Answer 1

It will be $(c\cos(\alpha),c\sin(\alpha))$

The distance of the point from the origin $(0,0)$ is $c$.

Initially, the angle was $0^o$ and now it is $\alpha^o$

So, the point becomes $(c\cos(\alpha),c\sin(\alpha))$