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=(adj)/(hyp) \\\\ \cos(\frac{\pi}6)=\frac{x}5 \\\\ \frac{√(3)}2=\frac{x}5 \\\\ \frac{5√(3)}2=x`

As for y...


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


`\boxed{(\frac{5√(3)}2,\ \frac{5}2)}`