Question

What is the Cartesian form of `( 8 , (13pi)/6 )`?

Answer 1

Cartesian form of `(8, (13pi)/6)`is`=(4 sqrt3, 4)`

Explanation:

Given `r=8`
`theta=(13pi)/6`
Formulas;
`x=r*cos theta` and `y=r*sin theta`

Solve for the Cartesian coordinates:
For x:
`x=r cos theta`
`x=8*cos ((13 pi)/6)`
`x=4sqrt(3)`

For y:
`y=r sin theta`
`y=8*sin ((13 pi)/6)`
`y=8*(1/2)`
`y=4`

Final answer `(4sqrt(3), 4)`