I know the image below isn't to scale and that the angle isn't quite at the centre point but can we just imagine it is picture perfect….
I know the coordiantes and point (x,y) lets say they are (1,1) for simplicity, I also know the angle at centre point is 15 degrees. What is the method I use to find the coordinates at x1,y1.
Please note this is not doing my 'homework' for me, despite it being broad. It is part of a project I am on at work and I have simply came to a mind block with this common calculation – cant seem to find it on the internet without it going into arc lengths and pythagoras (which I will later need)
Best Answer
Let's call the radius $r$. Since the original point $(x,y)$ is on the circle, you can find some angle $\alpha$ such that $x = r\cos\alpha$ and $y = r\sin\alpha$. You could get $\alpha$ by calculating
atan2(x,y), for example.Then the new point $(x_1,y_1)$ is at angle $\beta = \alpha - 15^\circ$, so its coordinates are $x_1 = r\cos\beta$ and $y_1 = r\sin\beta$.
Or, a bit more directly: $$ x_1 = \; x\cos 15^\circ + y\sin 15^\circ \\ y_1 = -x\sin 15^\circ + y\cos 15^\circ \\ $$ This assumes that positive angles (like your 15 degrees) correspond to clockwise movement.