What is the polar form of #(2,3)#?

Answer 1

#(sqrt13,tan^{-1}(3/2))#

To write in polar form, you need to know

To solve 1. we use Pythagoras Theorem

#r = sqrt{2^2 + 3^2}#
#= sqrt13#

To solve 2. we first find the quadrant that the point lies in.

#x# is positive and #y# is positive #=># quadrant I
Then we can find the angle by directly taking inverse tangent of #y/x#. (Note that this is only applicable to quadrant I).
#theta = tan^{-1}(3/2)#
#~~ 0.983# (in radians)
Therefore, the polar coordinate is #(sqrt13,tan^{-1}(3/2))#
Note that the answer above is not unique. You can add any integer multiples of #2pi# to #theta# to get other representations of the same point.
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Answer 2

The polar form of the point (2,3) in the Cartesian coordinate system can be found using the conversion formulas from rectangular (Cartesian) coordinates to polar coordinates:

r = sqrt(x^2 + y^2) θ = arctan(y/x)

For the point (2,3): r = sqrt(2^2 + 3^2) = sqrt(4 + 9) = sqrt(13) θ = arctan(3/2) = approximately 56.31 degrees (in radians: approximately 1.25 radians)

Therefore, the polar form of the point (2,3) is (sqrt(13), 56.31°).

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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.

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.

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.

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.

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