A circle of radius 10 units is shown in figure. The coordinates of point P is : 

Coordinates of a general point in xy plane are $\mathrm{x}=\mathrm{r} \cos \mathrm{\theta }, \mathrm{y}=\mathrm{r} \sin \mathrm{\theta }$, where r is the distance from origin and $\mathrm{\theta }$ is the angle made by +x-axis.
$$\begin{gathered} \mathrm{x}=\mathrm{r} \mathrm{cos\theta }=10 \cos 53°=10\left(\frac{3}{5}\right)=6, \\ \mathrm{y}=\mathrm{r} \mathrm{sin\theta }=10 \sin 53°=10 \left(\frac{4}{5} \right)= 8 \end{gathered}$$