# What is the polar form of #( -4,5 )#?

The polar form of (-4,5) has

You can use Pythagoras theorem or the complex numbers. I'm gonna use the complex numbers because it is simpler to write down and to explain as I always do that and english is not my mother language.

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The polar form of the point ( (-4, 5) ) in Cartesian 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 segment connecting the origin and the point.

To find ( r ), we use the distance formula:

[ r = \sqrt{(-4)^2 + 5^2} = \sqrt{16 + 25} = \sqrt{41} ]

To find ( \theta ), we use the arctangent function:

[ \theta = \arctan\left(\frac{5}{-4}\right) ]

Since ( (-4, 5) ) lies in the second quadrant, we need to add ( \pi ) to the angle obtained from the arctangent to get the correct angle in the polar form.

[ \theta = \arctan\left(\frac{5}{-4}\right) + \pi ]

Therefore, the polar form of ( (-4, 5) ) is ( (\sqrt{41}, \arctan\left(\frac{5}{-4}\right) + \pi) ).

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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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