Question

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

Answer 1

Answer:

  C.  (8.5, 14.72)

Step-by-step 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)

__

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.