Find the exact value of $cos(frac{5pi}{6})$ using the unit circle.
Answer 1
Emily Hall
To find the exact value of $\cos(\frac{5\pi}{6})$, we first determine the location of the angle on the unit circle.
The angle $\frac{5\pi}{6}$ is in the second quadrant. In the unit circle, the cosine of an angle in the second quadrant is negative.
The reference angle for $\frac{5\pi}{6}$ is $\pi – \frac{5\pi}{6}$, which simplifies to $\frac{\pi}{6}$.
The cosine of $\frac{\pi}{6}$ is $\frac{\sqrt{3}}{2}$. Therefore, $\cos(\frac{5\pi}{6}) = – \frac{\sqrt{3}}{2}$.
$\cos\left(\frac{5\pi}{6}\right) = – \frac{\sqrt{3}}{2}$
Answer 2
Isabella Walker
Let’s find $cos(frac{5pi}{6})$ using the unit circle. We know that $frac{5pi}{6}$ is equivalent to 150 degrees, which lies in the second quadrant.
In the second quadrant, the cosine value is negative. The reference angle here is $180^circ – 150^circ = 30^circ$.
The cosine of 30 degrees is $frac{sqrt{3}}{2}$. Therefore, $cos(150^circ) = – frac{sqrt{3}}{2}$.
This means:
$cosleft(frac{5pi}{6}
ight) = – frac{sqrt{3}}{2}$
Answer 3
Emma Johnson
We need to find $cos(frac{5pi}{6})$.
The angle $frac{5pi}{6}$ is in the second quadrant, and its reference angle is $frac{pi}{6}$.
Since cosine is negative in the second quadrant,
$cosleft(frac{5pi}{6}
ight) = – frac{sqrt{3}}{2}$
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