Question

What is the Cartesian form of `( 9 , (16pi)/6 )`?

Answer 1

Cartesian form `(x, y)=(-9/2, (9sqrt3)/2)`

Explanation:

We start from the given `(9, (16pi)/6)`

`r=9` and `theta=(16pi)/6=(8pi)/3`

solve for x

`x=r*cos theta`
`x=9*cos ((8pi)/3)=9*cos ((2pi)/3)=9*(-1/2)=-9/2`

solve for y

`y=r*sin theta`
`y=9*sin ((8pi)/3)=9*sin ((2pi)/3)=9*(sqrt3/2)=(9sqrt3)/2`

God bless....I hope the explanation is useful.