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What is the polar form of #(1,18)#?

Answer 1

Isaiah Allen

(18, 1.5)

Polar format: (r, #theta#)

#r=sqrt(x^2+y^2)#

#theta = tan^-1(y/x)#

apply both formulas when going from Cartesian -> polar

#sqrt(1^2+18^2) = sqrt(325) ~~ 18.0#

#theta = tan^-1(18/1) = tan^-1(18) ~~ 1.5 radians#

Thus our answer of:

Polar format of (1,18) Cartesian is:

(18, 1.5)

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Answer 2

Evelyn Agard

#(r,theta)=(5sqrt(13),arctan(18))#

Given Cartesian coordinates #(x,y)# in Quadrant I

#r=sqrt(x^2+y^2)# and #theta=arctan(y/x)#

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Answer 3

Ezekiel Alexander

The polar form of the complex number (1,18) is 1∠18°.

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Answer 4

Christopher Agresta

To convert the Cartesian coordinates ( (1, 18) ) to polar form, we use the formulas:

[ r = \sqrt{x^2 + y^2} ] [ \theta = \arctan\left(\frac{y}{x}\right) ]

Substituting the given coordinates: [ r = \sqrt{1^2 + 18^2} = \sqrt{1 + 324} = \sqrt{325} ]

[ \theta = \arctan\left(\frac{18}{1}\right) = \arctan(18) ]

Therefore, the polar form of ( (1, 18) ) is ( (\sqrt{325}, \arctan(18)) ).

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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.