Answer
The sides of the triangle that give the coordinates of point $P$ are the opposite and adjacent sides to the central angle.
The coordinates are $P=(2\sqrt 2, 2\sqrt 2)$.
Work Step by Step
To form point $P$, we trace a line from the x and y axis until a right triangle is formed. This lines would be the opposite and adjacent sides from the $45^{\circ}$ angle.
To calculate the coordinates of $P$, remember the formula for polar coordinates: $P=(r\cos\theta, r\sin\theta)$
In this case, $r=4$ and $\theta=45^{\circ}$
Substituting in the formula,
$P=(4\cos(45^{\circ}), 4\sin(45^{\circ}))$
$P=(4*\frac{\sqrt 2}{2}, 4*\frac{\sqrt 2}{2})$
$P=(2\sqrt 2, 2\sqrt 2)$
