How would you match the polar coordinates with the corresponding rectangular coordinates?

Question

1. (2, π/2)
2. (2, 7π/6)
3. (2, 7π/4)
4. (-2, π/4)
5. (-2, 5π/6)
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a. (-2^1/2, -2^1/2, )
b. (0, 2)
c. (3^1/2, -1)
d. (2^1/2, -2^1/2, )
e. (-3^1/2, -1)
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Fill in with each letter.

1. ?
2. ?
3. ?
4. ?
5. ?

Answer 1

polar coordinates: (r,θ)
equivalent rectangular coordinates: (r*cos(θ), r*sin(θ))

Answer 2

The rectangular coords are (r cos θ, r sin θ).
So we get
1. (2 cos π/2, 2 sin π/2) = (2(0), 2(1)) = (0, 2) = b.
2. (2 cos 7π/6, 2 sin 7π/6) = (2(-√3/2), 2(-1/2)) = (-√3, -1) = e.
and so on. The full list is
1. b
2. e
3. d
4. a
5. c