Question

Convert (5, pi/6) to rectangular coordinates

Answer 1

Polar coordinates are written as the distance of the point to the origin and its angle of elevation around the unit cirlce.

Draw a right triangle with an angle of $\frac{\pi}6$ and a hypotenuse with a length of 5.

You can use trigonometric ratios to find the legs of this triangle, which are the x and y coordinates of the point.

$\cos=\frac{adj}{hyp} \\\\ \cos(\frac{\pi}6)=\frac{x}5 \\\\ \frac{\sqrt{3}}2=\frac{x}5 \\\\ \frac{5\sqrt{3}}2=x$

As for y...

$\sin=\frac{opp}{hyp}\\\\\sin(\frac{\pi}6) = \frac{y}5 \\\\ \frac{1}2=\frac{y}5 \\\\ \frac{5}2=y$

$\boxed{(\frac{5\sqrt{3}}2,\ \frac{5}2)}$