Question

What is the Cartesian form of `(24,(5pi)/6))`?

Answer 1

Answer: `(-12sqrt(3),12)`

Explanation:

Consider the following formulas to convert from polar to Cartesian:
`x=rcos(theta)`
`y=rsin(theta)`

Since we are given the polar coordinate in `(r,theta)` form, we can simply substitute into the above formulas:
`x=24cos((5pi)/6)`
`y=24sin((5pi)/6)`

Now, we can simplify each individually:
`x=24cos((5pi)/6)`
`=24(-sqrt(3)/2)` using our special unit circle trig values
`=-12sqrt(3)`

`y=24sin((5pi)/6)`
`=24(1/2)` using our special unit circle trig values
`=12`

Therefore, we have the point `(-12sqrt(3),12)` in Cartesian form.