Convert the point (2,π/3)from polar to Cartesian coordinates?

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hev1 · sankarankalyanam
Mar 27, 2018

The polar coordinates #(2, pi/3)# is approximately #color(maroon)(((1, sqrt3)))# in Cartesian form.

Explanation:

To convert a pair of coordinates #(r, theta)# in polar form to Cartesian coordinates, we use the equations #x = cos(theta)*r# and #y=sin(theta)*r#.

![https://study.com/academy/lesson/http://trigonometric-function-values-of-special-angles.html](https://useruploads.socratic.org/Js2cZNKRTcKjILnsbFUu_trigonometric%20values.jpg)

Plugging in #2# for #r# and #pi/3# for #theta#:

#x = cos(pi/3)*2#

#x ~~ color(maroon)((1/2)) * 2 color(green)(" as " cos (pi/3) = (1/2)#

#x ~~ color(maroon)(1)#

#y = sin(pi/3)*2#

#y ~~ color(maroon)(sqrt3/2) * 2color(green)(" as " cos (pi/3) = (1/2)#

#y ~~color(maroon)(sqrt3 = 1.732#

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