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 $θ$ $theta$ : OA=25, $θ = 210^{\circ}$ $theta=210^circ$ ?

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Answer 1 · 2018-03-04T11:59:43

Coordinates of $A = (- \frac{25 \sqrt{3}}{2}, - \frac{25}{2})$ $color(green)(A = (-(25sqrt3)/2, -25/2)$

$- - \to O A = 25, θ = 210^{\circ}$ $vec(OA) = 25, theta = 210^@$

To find x & y coordinates of point A.

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Point A is in third quadrant as $θ$ $theta$ is between $180^{\circ}$ $180^@$ & $270^{\circ}$ $270^@$

Hence, both x , y coordinates are negative.

$A_{x} = ¯ ¯¯¯¯ ¯ O A cos θ = 25 \cdot cos 210 = 25 \cdot (- cos 30)$ $A_x = bar(OA) cos theta = 25 * cos 210 = 25 * (- cos 30)$

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

$A_{x} = - \frac{25 \cdot \sqrt{3}}{2}$ $A_ x = -(25 * sqrt3) / 2$

$A_{y} = ¯ ¯¯¯¯ ¯ O A sin θ = 25 \cdot sin 210 = 25 \cdot (- sin 30)$ $A_y = bar(OA) sin theta = 25 * sin 210 = 25 * (- sin 30)$

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

$A_{y} = - (25 \cdot (\frac{1}{2})) = \frac{25}{2}$ $A_y = -(25 * (1/2)) = 25/2$

Coordinates of $A = (- \frac{25 \sqrt{3}}{2}, - \frac{25}{2})$ $color(green)(A = (-(25sqrt3)/2, -25/2)$

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 thetaθtheta: OA=25, theta=210^circθ=210∘theta=210^circ?