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

1 Answer
Y
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.

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