# How do you change rectangular coordinates to polar coordinates?

You can use:

#r=sqrt{x^2+y^2}#

If

#theta=tan^{-1}(y/x)# .If

#(x,y)# is in the second or third quadrant,

#theta=tan^{-1}(y/x)+pi# .

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To change rectangular coordinates (x, y) to polar coordinates (r, θ), you can use the following formulas:

r = √(x^2 + y^2) θ = arctan(y / x) or θ = arctan2(y, x)

Where:

- r is the distance from the origin to the point.
- θ is the angle formed by the positive x-axis and the line segment connecting the origin to the point.
- arctan denotes the arctangent function, and arctan2(y, x) is a function available in many programming languages that returns the angle whose tangent is y / x, with signs of y and x determining the quadrant of the result.

Make sure to consider the appropriate quadrant for the angle θ.

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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.

- What is the Cartesian form of #( 3 , ( - 15pi)/2 ) #?
- What is the slope of the tangent line of #r=5theta+cos(-theta/3-(pi)/2)# at #theta=(-pi)/6#?
- What is the slope of the tangent line of #r=(sin^2theta)/(-thetacos^2theta)# at #theta=(pi)/4#?
- What is the distance between the following polar coordinates?: # (4,(-7pi)/12), (2,(pi)/8) #
- What is the distance between the following polar coordinates?: # (4,(-11pi)/12), (1,(-7pi)/8) #

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