SOLUTION: Convert the given polar coordinates to Cartesian coordinates. 7, 4𝜋 3

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Question 1204907: Convert the given polar coordinates to Cartesian coordinates.
7,
4𝜋
3

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Convert the given polar coordinates to Cartesian coordinates.
When we know a point in polar coordinates (r, theta).

given:
(r, theta)=(7,4pi%2F3)
=> r=7 and theta=4pi%2F4
to convert from polar coordinates (r, theta) to cartesian coordinates (x, y) :
x+=+r+%2A+cos%28+theta+%29
y+=+r+%2Asin%28+theta+%29
so,
x+=+7+%2A+cos%28+4pi%2F3%29
x+=+7+%2A+%28+-1%2F2%29
x+=+-7%2F2

y+=+7+%2Asin%28+4pi%2F3+%29
y+=+7+%2A%28-sqrt%283%29%2F2%29
y+=+%28-7sqrt%283%29%2F2%29
Cartesian Coordinates:
(x, y)=(-7%2F2,+-%287sqrt%283%29%29%2F2)