What are the coordinates for the point $p (\frac{11 π}{3})$ $p((11pi)/3)$ where $p (θ) = (x, y)$ $p(theta)=(x,y)$ is the point where the terminal arm of an angle $θ$ $theta$ intersects the unit circl?

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What are the coordinates for the point $p (\frac{11 π}{3})$ $p((11pi)/3)$ where $p (θ) = (x, y)$ $p(theta)=(x,y)$ is the point where the terminal arm of an angle $θ$ $theta$ intersects the unit circl?

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Answer 1 · 2018-03-19T03:30:12

$P (\frac{1}{2}, - \frac{\sqrt{3}}{2})$ $P(1/2, - sqrt3/2)$

Explanation:

By the definitions of trig functions, the point P has as coordinates: -
P(x, y)
$x = cos (\frac{11 π}{3})$ $x = cos ((11pi)/3)$ , and $y = sin (\frac{11 π}{3})$ $y = sin ((11pi)/3)$
Trig table and unit circle give -->
$x = cos (\frac{11 π}{3}) = cos (- \frac{π}{3} + 4 π) = cos (- \frac{π}{3}) = cos (\frac{π}{3}) = \frac{1}{2}$ $x = cos ((11pi)/3) = cos (-pi/3 + 4pi) = cos (-pi/3) = cos (pi/3) = 1/2$
$y = sin (\frac{11 π}{3}) = sin (- \frac{π}{3} + 4 π) = sin (- \frac{π}{3}) =$ $y = sin ((11pi)/3) = sin (-pi/3 + 4pi) = sin (- pi/3) =$
$- sin (\frac{π}{3}) = - \frac{\sqrt{3}}{2}$ $- sin (pi/3) = -sqrt3/2$
Answer: $P (\frac{1}{2}, - \frac{\sqrt{3}}{2})$ $P(1/2, -sqrt3/2)$ .
Note. P is in Quadrant 4.

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What are the coordinates for the point $p (\frac{11 π}{3})$ $p((11pi)/3)$ where $p (θ) = (x, y)$ $p(theta)=(x,y)$ is the point where the terminal arm of an angle $θ$ $theta$ intersects the unit circl?

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Explanation:

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Explanation:

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What are the coordinates for the point $p (\frac{11 π}{3})$ $p((11pi)/3)$ where $p (θ) = (x, y)$ $p(theta)=(x,y)$ is the point where the terminal arm of an angle $θ$ $theta$ intersects the unit circl?