# What is the polar form of #( 4,9 )#?

The triangle

Use the Tangent Function to find the desired angle

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is the hypotenuse of a right angled triangle with

forming the other two sides that enclose the right angle.

The side on the x axis has length 4, and that on the y axis has length 9, so that, by the Pythagorean relationship, the length of the hypotenuse is

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To convert the Cartesian coordinates ((4, 9)) to polar coordinates, we use the formulas:

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

Substitute (x = 4) and (y = 9) into these formulas:

[ r = \sqrt{4^2 + 9^2} = \sqrt{16 + 81} = \sqrt{97} ] [ \theta = \arctan\left(\frac{9}{4}\right) ]

Now, to find (\theta), you can use a calculator to find the arctan or inverse tangent of (\frac{9}{4}).

So, the polar form of the point ((4, 9)) is ((\sqrt{97}, \arctan\left(\frac{9}{4}\right))).

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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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