Question

Find the rectangular coordinates of the point with the polar coordinates ordered pair negative 7 comma 5 pi divided by 3.

A) ordered pair 7 divided by 2 comma negative 7 divided by 2
B) ordered pair 7 square root 3 divided by 2 comma negative 7 divided by 2
C) ordered pair negative 7 divided by 2 comma 7 divided by 2
D) ordered pair negative 7 divided by 2 comma 7 square root 3 divided by 2

Answer 1

we have that

(r, ∅)----------> (-7, 5 pi/3)

we know that
5 pi/3--------> 300°-----------> -60°
To convert polar cordinates in rectangular one with use the following formula:
x=r*cos ∅------> x=-7*cos -60°-------> x=-7*(1/2)------> x=-7/2
y=r*sin ∅-------> y=-7*sin -60-------> y=-7*(-√3)/2----> y=7√3/2

the answer is the option
D) ordered pair negative 7 divided by 2 comma 7 square root 3 divided by 2