How does one find the rectangular coordinates of a point with polar coordinates (-2, 11pi/6)?

1 Answer
Apr 27, 2018

(-sqrt(3),1)

Explanation:

In general polar coordinates are (r,theta)
for some radius r and angle theta counter-clockwise from the x-axis. This forms a right triangle with hypotenuse r connecting the origin and (r,theta).

The Pythagorean trigonometric identity is:
sin^2(theta)+cos^2(theta)=1
Multiplying both sides by r gives us :
rsin^2(theta)+rcos^2(theta)=r

Going back to the triangle, this tells us that if the hypotenuse is r then the side going vertically up (y-coordinate) is rsin(theta)
and the side going horizontal (x-coordinate) is rcos(theta).
Therefore (x,y) = (rcos(theta),rsin(theta)).
Since the angle is given in a multiple of pi, I hope you mean radians.

We have (r,theta) = (-2,(11pi)/6) so (x,y) = (-2cos((11pi)/6),-2sin((11pi)/6)) = (-sqrt(3),1)