# How to calculate $B(x_1,y_1)$ when $\alpha$ and $A(x_0,y_0)$ are known?

In case one want to calculate $\alpha$ angle between $AB$ vector and $x$ axis, it can calculate $\alpha=arctan2(x_1-x_0,y_1-y_0)$. Thus, for example for $A(0,0)$ and $B(10,10)$ one will get $\alpha$ equal to 45°. Is there a way to calculate $x_1,y_1$ coordinates when $\alpha$ angle and $x_0,y_0$ are given?

• You need also the distance $AB$. – Emilio Novati Mar 11 '16 at 18:15
• Say, it is known and we can call it as $z$. – bluevoxel Mar 11 '16 at 18:16

If we know the distance $AB=r$ than we have: $$x_1=x_0+r\cos \alpha \qquad y_1=y_0+r \sin \alpha$$
• It is worth to mention that $\alpha$ has to be in radians. – bluevoxel Mar 11 '16 at 18:40
• No matter! $\alpha$ cam be in radians or degree, anyway $\cos \alpha$ and $\sin \alpha$ have one well defined value for given $\alpha$. – Emilio Novati Mar 11 '16 at 19:01