Question

How do you write in simplest radical form the coordinates of point A if A is on the terminal side of angle in standard position whose degree measure is `theta`: OA=25, `theta=210^circ`?

Answer 1

Coordinates of `color(green)(A = (-(25sqrt3)/2, -25/2)`

Explanation:

`vec(OA) = 25, theta = 210^@`

To find x & y coordinates of point A.

Point A is in third quadrant as `theta` is between `180^@` & `270^@`

Hence, both x , y coordinates are negative.

`A_x = bar(OA) cos theta = 25 * cos 210 = 25 * (- cos 30)`

as `cos(180 + 30) = - cos 30`

`A_ x = -(25 * sqrt3) / 2`

`A_y = bar(OA) sin theta = 25 * sin 210 = 25 * (- sin 30)`

as `sin(180 + 30) = - sin 30`

`A_y = -(25 * (1/2)) = 25/2`

Coordinates of `color(green)(A = (-(25sqrt3)/2, -25/2)`