Section 10.3: Polar Coordinates

What is the first step in plotting a point using polar coordinates?

• Plot the point directly on the grid.

• Identify the polar axis.

• Determine the radius from the pole.

• Measure the angle in radians from the polar axis.

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CCSS.HSN.CN.B.4

How do you convert polar coordinates (r, θ) to rectangular coordinates (x, y)?

• x = r sec(θ), y = r csc(θ)

• x = r sin(θ), y = r cos(θ)

• x = r cos(θ), y = r sin(θ)

• x = r tan(θ), y = r cot(θ)

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CCSS.HSN.CN.B.4

Which equation represents the conversion from rectangular coordinates to polar coordinates for the radius r?

• r = tan(y/x)

• r = x + y

• r = x^2 + y^2

• r = sqrt(x^2 + y^2)

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CCSS.HSN.CN.B.4

What is the polar form of the Cartesian equation x^2 + y^2 = 9?

• r = sqrt(9)

• r = 6

• r = 9

• r = 3

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CCSS.HSN.CN.B.4

How is the angle θ calculated in polar coordinates when converting from rectangular coordinates?

• θ = tan^-1(y/x)

• θ = sin^-1(y/r)

• θ = cos^-1(x/r)

• θ = sec^-1(x/y)

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CCSS.HSN.CN.B.4

What is the result of converting the polar coordinates (3, π/2) to rectangular coordinates?

• (3, 0)

• (0, 3)

• (0, -3)

• (-3, 0)

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CCSS.HSN.CN.B.4

Which of the following is a correct representation of a point with a negative radius in polar coordinates?

• Plot the point in the opposite direction of the angle.

• Keep the radius positive and double the angle.

• Halve the angle and double the radius.

• Double the radius and keep the angle same.

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CCSS.HSN.CN.B.4

What does the polar equation r = 2 sec(θ) represent in Cartesian coordinates?

• y = 2

• x = 4

• y = 4

• x = 2

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CCSS.HSN.CN.B.4

How is a circle with radius 3 represented in polar coordinates?

• r = 6

• r = 9

• r^2 = 9

• r = 3

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CCSS.HSN.CN.B.4

What is the polar form of the Cartesian equation y = 3x + 2?

• r(3sin(θ) + 2cos(θ)) = 1

• r(sin(θ) - 3cos(θ)) = 2

• r(2sin(θ) - 3cos(θ)) = 1

• r(3sin(θ) - 2cos(θ)) = 1

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CCSS.HSN.CN.B.4