How do you convert #(2,(-7pi)/6)# into cartesian form?

1 Answer
Y
May 10, 2017

Use #x=rcostheta# and #y=rsintheta#. Answer: #(-sqrt(3),1)#

Explanation:

Original problem: Convert #(2, -(7pi)/6)# to Cartesian

To convert from polar coordinates to Cartesian form, we use the equations #x=rcostheta# and #y=rsintheta#.

Since we have #(r,theta)#, we can simply substitute into the above formulas:
#x=2cos(-(7pi)/6)#
Using our unit circle trig values
#x=2(-sqrt(3)/2)#
#x=-sqrt(3)#

#y=2sin(-(7pi)/6)#
Using our unit circle trig values
#y=2(1/2)#
#y=1#

Therefore our final answer in Cartesian form is: #(-sqrt(3),1)#

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