What is the Cartesian form of #(18,(-51pi)/8))#?

Answer 1

Ezra Adams

#(6.888, -16.630)#

We're asked to find the Cartesian (rectangular) form of a polar coordinate.

To do this, we can use the equations

#x = rcostheta#

#y = rsintheta#

#x = 18cos((-51pi)/8) = color(red)(6.888#

#y = 18sin((-51pi)/8) = color(blue)(-16.630#

The rectangular form is thus

#(color(red)(6.888), color(blue)(-16.630))#

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Answer 2

Ezekiel Alexander

The Cartesian form of the point (18, (-51π)/8) is (18cos((-51π)/8), 18sin((-51π)/8)). Evaluating the trigonometric functions, we get:

(18cos((-51π)/8), 18sin((-51π)/8)) = (18cos(-6.375π), 18sin(-6.375π)) = (18cos(0.625π), 18sin(0.625π)) = (18cos(0.625π), -18sin(0.625π)) = (18(-0.707), -18(0.707)) = (-12.726, -12.726)

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.