Question

What is `(5,8)` in polar coordinates?

Answer 1

The polar coordinates would be `(r, theta)` or `(sqrt89, theta)` where `theta` is defined by the relation `tan theta=1.6`

Explanation:

Cartesean and Polar coordinates are related by x= `r cos theta` and y=`rsin theta`

Hence `rcos theta= 5`
`rsin theta=8`

Squaring and adding the above two equations would give `r^2=89` thus r= `sqrt89`

Dividing the second equation by the first one would give `tan theta= 8/5= 1.6`

The polar coordinates would be `(r, theta)` or `(sqrt89, theta)` where `theta` is defined by the relation `tan theta=1.6`