Converting Cartesian Coordinates to Polar Coordinates

This tutorial explains how to convert Cartesian coordinates to polar coordinates. It covers plotting points on a coordinate plane, understanding quadrants, and using formulas to calculate the polar coordinates (r, θ). Two examples are provided: one in the third quadrant and another in the fourth quadrant. The tutorial also includes tips for handling points on axes and emphasizes the importance of reference angles in determining the correct angle θ.

What is the condition for r in polar coordinates?

• r can be negative or positive

• r is always zero

• r must be greater than zero

• r must be less than zero

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CCSS.6.NS.C.6B

In which quadrant is the point (-3, -2) located?

• First quadrant

• Second quadrant

• Third quadrant

• Fourth quadrant

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CCSS.HSN.CN.B.4

What formula is used to calculate r from Cartesian coordinates?

• r = x + y

• r = x * y

• r = x - y

• r = sqrt(x^2 + y^2)

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CCSS.HSN.CN.B.4

How is the reference angle 'a' determined?

• a = arctan(x/y)

• a = arctan(y/x)

• a = arctan(x^2 + y^2)

• a = arctan(x - y)

What is the approximate value of theta for the point (-3, -2)?

• 5.7 radians

• 3.7 radians

• 2.5 radians

• 4.5 radians

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CCSS.6.NS.C.6B

In which quadrant is the point (3, -2) located?

• Fourth quadrant

• Third quadrant

• Second quadrant

• First quadrant

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CCSS.HSF.TF.A.2

What is the formula for theta in the fourth quadrant?

• theta = pi + a

• theta = pi - a

• theta = 2pi + a

• theta = 2pi - a

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CCSS.HSF.TF.A.2

What is the approximate value of theta for the point (3, -2)?

• 5.7 radians

• 6.7 radians

• 4.7 radians

• 3.7 radians

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CCSS.HSN.CN.B.4

What is the polar coordinate form of the point (3, -2)?

• (sqrt(13), 4.5)

• (sqrt(13), 5.6952)

• (sqrt(13), 6.5)

• (sqrt(13), 3.7296)

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CCSS.6.NS.C.6C

What should be done if a point falls on one of the axes?

• Assume the point is in the first quadrant

• Ignore the point

• Use the same formula for all quadrants

• Plot the point and analyze the graph

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CCSS.6.NS.C.6C