Question

How do you change the polar coordinate `(4,45^o)` into rectangular coordinates?

Answer 1

The rectangular coordinates are `(2sqrt2,2sqrt2)`

Explanation:

If the polar coordinates are `(r.theta)`
the the rectangular coordinates are
`x=rcostheta`
and `y=rsintheta`
So here we have
`x=4cos45º=4*sqrt2/2=2sqrt2`
and `y=4sin45º=4*sqrt2/2=2sqrt2`