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

1 Answer
May 14, 2017

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.