Find the cosecant of the angle $frac{pi}{6}$ on the unit circle.
Answer 1
Maria Rodriguez
To find the cosecant of the angle $\frac{\pi}{6}$ on the unit circle, we first need to find the sine of $\frac{\pi}{6}$.
On the unit circle, the sine of $\frac{\pi}{6}$ is $\frac{1}{2}$.
The cosecant is the reciprocal of the sine.
So, the cosecant of $\frac{\pi}{6}$ is:
$\csc\left(\frac{\pi}{6}\right) = \frac{1}{\sin\left(\frac{\pi}{6}\right)} = \frac{1}{\frac{1}{2}} = 2$
Answer 2
Michael Moore
First, we determine the sine of $frac{pi}{6}$ from the unit circle.
We know that:
$sinleft(frac{pi}{6}
ight) = frac{1}{2}$
Then, we find the cosecant, which is the reciprocal of the sine:
$cscleft(frac{pi}{6}
ight) = frac{1}{sinleft(frac{pi}{6}
ight)} = frac{1}{frac{1}{2}} = 2$
Thus, the cosecant of $frac{pi}{6}$ is $2$.
Answer 3
Matthew Carter
From the unit circle, we have:
$sinleft(frac{pi}{6}
ight) = frac{1}{2}$
The cosecant is the reciprocal:
$cscleft(frac{pi}{6}
ight) = frac{1}{sinleft(frac{pi}{6}
ight)} = 2$
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