Question

How do you find the rectangular coordinate of the following point (5,300)?

Answer 1

x- coordinate =5 and y- coordinate=300

Answer 2

If the polar co-ordinates `(r, theta)=(5, 300^o)`, the rectangular co-ordinates `(x, y)=(5/2, -5sqrt3/2)`.

Explanation:

`x=r cos theta and y=r sin theta`.

Here, r = 5 and `theta=300^o`.
`cos 300^o=cos(360^o-60^o)=cos 60^o=1/2`
`sin 300^o=sin(360^o-60^o)=-sin 60^o=-sqrt3/2`.
So, `(x, y) = (5/2, -5sqrt3/2)`.