30 POINTS
Find the rectangular coordinates of the point with the polar coordinates ordered pair negative 3 comma 5 pi divided by 3 . (1 point)
ordered pair negative 3 divided by 2 comma 3 divided by 2
ordered pair 3 square root 3 divided by 2 comma negative 3 divided by 2
ordered pair negative 3 divided by 2 comma 3 square root 3 divided by 2
ordered pair 3 divided by 2 comma negative 3 divided by 2

Question

25-02-2021
Mathematics

contestada

30 POINTS
Find the rectangular coordinates of the point with the polar coordinates ordered pair negative 3 comma 5 pi divided by 3 . (1 point)
ordered pair negative 3 divided by 2 comma 3 divided by 2
ordered pair 3 square root 3 divided by 2 comma negative 3 divided by 2
ordered pair negative 3 divided by 2 comma 3 square root 3 divided by 2
ordered pair 3 divided by 2 comma negative 3 divided by 2

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aeriiiel aeriiiel · Answer 1 · 2021-02-25T12:10:35+01:00

The correct answer is C. ordered pair negative 3 divided by 2 comma 3 square root 3 divided by 2

(r,θ) = (x,y)
x = r * cosθ
y = r * sinθ
Since your θ is 5π3, set your calculator to radians before taking the sine and cosine.

(3 cos 5π / 3, 3 sin 5π / 3)
(3* 1 / 2, 3 * - sqrt(3) / 2)
(3 / 2, −3 sqrt (3) / 2)
if r = -3, then x is negative, y is positive.

Here are the following choices:
A. ordered pair negative 3 divided by 2 comma 3 divided by 2
B. ordered pair 3 square root 3 divided by 2 comma negative 3 divided by 2
C. ordered pair negative 3 divided by 2 comma 3 square root 3 divided by 2
D. ordered pair 3 divided by 2 comma negative 3 divided by 2