I need help with this Calculus Problem. Is there anyone who thinks they can solve it?

Question

Match the polar coordinates on the left with the corresponding rectangular coordinates on the right by placing the letter on the right in the appropriate box below.


Column preview

1. (2, pi/4) a. (1, -3^1/2)

2. (2, 5pi/6) b. (2^1/2, 2^1/2, )

3. (2, 3pi/2) c. (-3^1/2, 1)

4. (-2, 0) d. (0, -2)

5. (-2, 2pi/3) e. (-2, 0)


Matching Pairs

1. a, b, c, d, e
2. a, b, c, d, e
3. a, b, c, d, e
4. a, b, c, d, e
5. a, b, c, d, e


Answer

1.
2.
3.
4.
5.

Answer 1

I don't understand the second section...but I can do the matching portion for you.

1. b
2. c
3. a
4. e
5. d

Here's some explanation:

1: At θ = π/4, cos(θ) = sin(θ) = √2/2. 2 times that is just (√2, √2)

2. θ = 5π/6 is 30° away from 180°. cos(θ) = -√3/2 and sin(θ) = 1/2. Multiply each by 2 and you get (-√3, 1)

3. θ = 3π/2 is the same as 270°, or the -y axis. Since r is 2, you down the -y axis, which just gives you (0, -2)

4. θ = 0 is just the +x axis...with r = -2, you go backwards, down the -x axis. So you just get (-2, 0)

5. θ = 2π/3 is 120° - but r = -2 again. So you go across (add 180°) down to 300°, or -π/3 radians. cos(θ) = 1/2 and sin(θ) = -√3/2. Multiply by 2 to get (1, -√3)

Answer 2

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Answer 3

If that is a calculus problem, the schools have been dumbing down with a vengence.