Answer
$x=\frac{1}{2}( \cos\theta+ 1)$
$y=\frac{1}{2}(\sin\theta + \tan\theta)$
Work Step by Step
From the right triangles in the graph we determine the coordinates of the points $Q$ and $R$:
$Q(\cos\theta, \sin\theta)$
$R(1,\tan\theta)$
The point $P$ is middle point of $Q$ and $R$, therefore its coordinates are:
$x=\frac{1}{2}( \cos\theta+ 1)$
$y=\frac{1}{2}(\sin\theta + \tan\theta)$
$P\left(\frac{1+\cos\theta}{2},\frac{\sin\theta+\tan\theta}{2}\right)$
