Question

Find the corresponding rectangular coordinates for the polar point (4, -/6).

Answer 1

Is that supposed to be (4, -ƒÎ/6)?
If so, you would use this formula:

x = rcosӨ
y = rsinӨ

x = 4cos(-ƒÎ/6)
y = 4sin(-ƒÎ/6)

-ƒÎ/6 on the unit circle is the same as 11ƒÎ/6. The cosine (or x-value) for this angle is ã3/2, and the sine (or y-value) for this angle is -1/2.

x = 4(ã3/2)
y = 4(-1/2)

x = 2ã3
y = -2

Your answer is:

(2ã3, -2)