What is the Cartesian form of ( -5 , ( 7pi)/3 ) (−5,7π3)?

1 Answer
Fleur
Jul 5, 2017

In order to convert this polar coordinate into a Cartesian one, use the following formulas:

x=r cos thetax=rcosθ
y=r sin thetay=rsinθ

A polar coordinate is written in the form (r, theta)(r,θ), so in this case r=-5r=−5 and theta=(7π)/3, which can be written also as π/3.

Thus,
x = -5 cos ((π)/3) = -5/2
y = -5 sin ((π)/3) = -(5sqrt3)/2

The Cartesian coordinate would be (-5/2, -(5sqrt3)/2).

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