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#?

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Answer 1 · 2018-03-04T11:59:43

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

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

To find x & y coordinates of point A.

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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)#