Question

What is the Cartesian form of `( -5 , ( 7pi)/3 )`?

Answer 1

In order to convert this polar coordinate into a Cartesian one, use the following formulas:

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

A polar coordinate is written in the form `(r, theta)`, so in this case `r=-5` and `theta=(7π)/3`, which can be written also as `π/3`.

Thus,
`x = -5 cos ((π)/3) = -5/2`
`y = -5 sin ((π)/3) = -(5sqrt3)/2`

The Cartesian coordinate would be `(-5/2, -(5sqrt3)/2)`.