Question

Find the coordinates of the point on a circle with radius 4 at an angle of 2pi/3

{Please help!!}

Answer 1

The coordinates of the point on a circle with radius 4 at an angle of
`(2\pi)/(3)` radians are x = -2 and y = 3.464.

Explanation:

This problem ask us to determine the rectangular coordinates from polar coordinates. The polar coordinates of the point in rectangular form is expressed by the following expression:

`(x,y) = (r\cdot \cos \theta, r\cdot \sin \theta)`

Where
`r` and
`\theta` are the radius of the circle and the angle of inclination of the point with respect to horizontal, measured in radians. If
`r = 4` and
`\theta = (2\pi)/(3)\,rad`, the coordinates of the point are:

`(x,y) = \left(4\cdot \cos (2\pi)/(3),4\cdot \sin (2\pi)/(3) \right)`

`(x,y) = (-2, 3.464)`

The coordinates of the point on a circle with radius 4 at an angle of
`(2\pi)/(3)` radians are x = -2 and y = 3.464.