NY Regents Geometry Polar Coordinates — practice questions

Explore 3 free Polar Coordinates questions in NY Regents Geometry Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Polar Coordinates questions and exercises with answers

Showing questions 1–3 of 3.

Which pair of formulas converts a polar point into rectangular coordinates?Read the answer and worked solution →What are the rectangular coordinates of the polar point with r equal to 6 and theta equal to pi?Read the answer and worked solution →Cluster the conics by eccentricityRead the answer and worked solution →

Worked practice questions

Which pair of formulas converts a polar point into rectangular coordinates?

x is r sin theta, y is r cos theta
x is r plus theta, y is r minus theta
x is r over theta, y is r times theta
x is r cos theta, y is r sin theta

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Correct answer: D. x is r cos theta, y is r sin theta

1. Drop a perpendicular from the point to the x-axis to form a right triangle. 2. The cosine of theta is the adjacent side over the hypotenuse, so x is r cos theta. 3. The sine of theta is the opposite side over the hypotenuse, so y is r sin theta. _Source: OpenStax Precalculus (CC BY 4.0), Ch 8 "Further Applications of Trigonometry", section 8.3 Polar Coordinates_

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What are the rectangular coordinates of the polar point with r equal to 6 and theta equal to pi?

The point (-6, 0)
The point (6, 0)
The point (0, 6)
The point (0, -6)

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Correct answer: A. The point (-6, 0)

1. Use x equal to r cos theta and y equal to r sin theta. 2. The cosine of pi is negative 1, so x is 6 times negative 1, which is negative 6. 3. The sine of pi is 0, so y is 6 times 0, which is 0. 4. The point is therefore (-6, 0), a half turn from the polar axis. 5. Answering (6, 0) treats the cosine of pi as positive 1 and lands on the wrong side. _Source: OpenStax Precalculus (CC BY 4.0), Ch 8 "Further Applications of Trigonometry", section 8.3 Polar Coordinates_

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Cluster the conics by eccentricity

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Items

Group
Ellipse
Item
e = 0
Group
Ellipse
Item
e = 0.4
Group
Ellipse
Item
e = 0.9
Group
Parabola
Item
e = 1
Group
Hyperbola
Item
e = 1.5
Group
Hyperbola
Item
e = 3

Groups

Item
Ellipse
Item
Parabola
Item
Hyperbola

Instructions

Drag each eccentricity chip into the curve that value produces.

_Source: OpenStax College Algebra (CC BY 4.0), Ch 8 "Analytic Geometry", section 8.5 Conic Sections in Polar Coordinates_

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