What are the coordinates for the point $p((5pi)/6)$ where $p(theta)=(x,y)$ is the point where the terminal arm of an angle $theta$ intersects the unit circl?

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Answer 1 · 2017-12-31T12:13:08

$p((5pi)/6)=(-sqrt(3)/2,1/2)$

$(5pi)/6$ has reference angle $pi/6$ because $pi-(5pi)/6 = pi/6$ .

So we know that:
$|cos((5pi)/6)| = cos(pi/6) = sqrt(3)/2$
$|sin((5pi)/6)| = sin(pi/6) = 1/2$

Since $(5pi)/6 in$ QII, we know that $cos((5pi)/6)<0$ and $sin((5pi)/6)>0$ .

Combining what we know, we have that $p((5pi)/6)=(-sqrt(3)/2,1/2)$ .

I recommend memorizing the entire Unit Circle as it's not that difficult and is extremely useful.

What are the coordinates for the point p((5pi)/6)p((5pi)/6) where p(theta)=(x,y)p(theta)=(x,y) is the point where the terminal arm of an angle thetatheta intersects the unit circl?