Question

What are the approximate rectangular coordinates for the point with polar coordinates `(5, 30°)`?

Answer 1

`((5sqrt3)/2,5/2)`

Explanation:

`(5,30) => (r,theta)`

A triangle with a 30 degree angle is a special triangle.

90 degrees corresponds with the side of length `2x`
60 degrees corresponds with the side of length `xsqrt3`
30 degrees corresponds with the side of length `1x`

90 also corresponds to the length of `r` which is 5.

`(cancel2x)/cancel2=5/2`

Which now shows that ...

90 degrees corresponds with the side of length `5`
60 degrees corresponds with the side of length `(5sqrt3)/2`
30 degrees corresponds with the side of length `5/2`

`x=5cos(30)=5((cancel5sqrt3/2)/cancel5)=(5sqrt3)/2`

`y=5sin(30)=cancel5((5/2)/cancel5)=5/2`

`((5sqrt3)/2,5/2)`

View this tutorial for another explanation of a similar problem.