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=sqrt3#, #theta=300^circ#?

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Answer 1 · 2018-03-04T07:18:54

Coordinates of #A (sqrt3/2, -3/2)#

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Given #theta = 300^@, OA ==sqrt 3#

To find the coordinates of #A(x,y)#

#300^@# is in fourth quadrant.

OA forms a triangle with x axis and the three angles are having the measurements of #30^@, 60^@, 90^@#.

Then the sides will be in the ratio #x : sqrt 3 x = 2x#

#x = bar(OA) cos theta = sqrt 3 * cos 300 = sqrt 3 cos -60#

#x = sqrt 3 cos 60 = (sqrt 3 * sqrt 1) / 2 = sqrt3 /2#

#y = bar(OA) sin theta = sqrt 3 sin 300 = - sqrt 3 sin 60#

#y = - (sqrt 3 * sqrt 3) / 2 = -3/2#