Question

What are the Cartesian coordinates of a point with polar coordinates (17, 60 degrees)?

A.
(7, 9)
B.
(14.72, 8.5)
C.
(8.5, 14.72)
D.
(9, 7)

Answer 1

C. (8.5, 14.72)

Explanation:

Answer 2

C. (8.5, 14.72)

Explanation:

You can translate the coordinates using ...

(x, y) = (r·cos(θ), r·sin(θ))

Filling in the given polar coordinates, (r, θ) = (17, 60°), we have ...

(x, y) = (17·cos(60°), 17·sin(60°)

(x, y) = (8.5, 14.72)

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If you sketch the vector, you realize that the short side of the triangle (the x-coordinate) is half the length of the hypotenuse (17). This is because you recognize the side-length relationships in a 30°-60°-90° triangle. Only one answer choice shows that value.