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What is the Cartesian form of #(36,pi)#?

Answer 1

#(-36,0)#

The formulas used to convert between polar and Cartesian co-ordinates are: #x=rcostheta# #y=rsintheta#

We are given the polar co-ordinate point #(r,theta)->(36,pi)#, so #r=36# and #theta=pi#. Making substitutions in the above formulas: #x=36cos(pi)=36*(-1)=-36# #y=36sin(pi)=36(0)=0#

Therefore, the point in the Cartesian plane is #(-36,0)#.

Intuitively, this result makes sense because #pi# is a half-circle rotation, so in the Cartesian plane an angle of #pi# corresponds to a point on the #x#-axis (and therefore #y=0#). A radius of #36# means the point is #36# units to the left or right of the origin, and since an angle of #+pi# is a counterclockwise rotation, it would mean the point is #36# units to the left (and therefore #-36#).

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Answer 2

Christopher Agresta

The Cartesian form of (36, π) is (36 cos(π), 36 sin(π)), which simplifies to (-36, 0).

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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.