Plot the Polar Coordinates

Question

Plot the Points with polar coordinates (-6,-π/6) and (2, 3π/2). Plot on the Unit Circle.

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Please help! I'm just not understanding this. Please explain! Thank you!

Answer 1

A point with polar coordinates (r, θ) has rectangular coordinates (rcosθ, rsinθ) and lies on the circle with center (0,0) and radius l r l.

The given points do not lie on the unit circle. The point with polar coordinates (-6, -π/6) lies on the circle centered at (0,0) with radius 6 and has rectangular coordinates (6cos(-π/6), 6sin(-π/6)) = (6(√3/2), 6(-1/2)) = (3√3, -3). The values √3/2 and -1/2 come form the point on the unit circle corresponding to the angle -π/6.

Similarly, the point with polar coordinates (2, 3π/2) lies on the circle centered at (0,0) with radius 2 and has rectangular coordinates (2cos(3π/2), 2sin(3π/2)) = (0, -2)