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=0.5, $θ = 180^{\circ}$ $theta=180^circ$ ?

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Answer 1 · 2018-04-07T19:10:12

$A (- 0.5, \frac{\sqrt{3}}{2})$ $A(-0.5,sqrt3/2)$

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$x$ $x$ -coordinate of point $A$ $A$ is $= O A = 0.5$ $=OA=0.5$

$y$ $y$ -coordinate of point $A$ $A$ is $A B$ $AB$

$cos ∠ A O B = \frac{O A}{O B} = \frac{0.5}{1} = 0.5$ $cos/_AOB=(OA)/(OB)=0.5/1=0.5$

$∠ A O B = arccos (0.5) = \frac{π}{3}$ $/_AOB=arccos(0.5)=pi/3$

$sin ∠ A O B = \frac{A B}{O B} = \frac{A B}{1} = A B$ $sin/_AOB=(AB)/(OB)=(AB)/1=AB$

$sin (\frac{π}{3}) = \frac{\sqrt{3}}{2}$ $sin(pi/3)=sqrt3/2$

$A B = \frac{\sqrt{3}}{2}$ $AB=sqrt3/2$

Therefore,

$A (- 0.5, \frac{\sqrt{3}}{2})$ $A(-0.5,sqrt3/2)$

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 θtheta: OA=0.5, θ=180∘theta=180^circ?