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What is the polar form of #( 24,2 )#?

Answer 1

Evelyn Agard

#(24,2) to (sqrt580,0.083)#

Convert #(24,2) to (r,theta)#

#r = sqrt(24^2+2^2)#

#r = sqrt(580)#

#theta = tan^-1(2/24)#

#theta ~~ 0.083" rad"#

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Answer 2

Scarlett Allison

The polar form of the point ( (24, 2) ) in rectangular coordinates is ( (r, \theta) ), where ( r ) is the distance from the origin to the point and ( \theta ) is the angle measured counterclockwise from the positive x-axis to the line connecting the origin and the point.

To find ( r ), use the formula:

[ r = \sqrt{x^2 + y^2} ]

In this case:

[ r = \sqrt{24^2 + 2^2} = \sqrt{580} ]

To find ( \theta ), use the formula:

[ \theta = \arctan\left(\frac{y}{x}\right) ]

In this case:

[ \theta = \arctan\left(\frac{2}{24}\right) = \arctan\left(\frac{1}{12}\right) ]

Thus, the polar form of ( (24, 2) ) is approximately ( (\sqrt{580}, \arctan(1/12)) ).

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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.