Find the value of $sec( heta)$ on the unit circle where $ heta = frac{2pi}{3}$
Answer 1
Olivia Lee
Given $\theta = \frac{2\pi}{3}$, we need to find $\sec(\theta)$ on the unit circle.
First, we determine the coordinates of the point on the unit circle at $\theta = \frac{2\pi}{3}$.
The coordinates are $\left(\cos\left(\frac{2\pi}{3}\right), \sin\left(\frac{2\pi}{3}\right)\right)$. Since $\cos\left(\frac{2\pi}{3}\right) = -\frac{1}{2}$, we have:
$\sec\left(\frac{2\pi}{3}\right) = \frac{1}{\cos\left(\frac{2\pi}{3}\right)} = \frac{1}{-\frac{1}{2}} = -2$
Thus, the value of $\sec\left(\frac{2\pi}{3}\right)$ is $-2$.
Answer 2
Thomas Walker
To find $secleft(frac{2pi}{3}
ight)$, we start by identifying $cosleft(frac{2pi}{3}
ight)$.
On the unit circle, $cosleft(frac{2pi}{3}
ight) = -frac{1}{2}$ because $frac{2pi}{3}$ lies in the second quadrant.
Then, $secleft(frac{2pi}{3}
ight)$ is the reciprocal of $cosleft(frac{2pi}{3}
ight)$:
$secleft(frac{2pi}{3}
ight) = frac{1}{cosleft(frac{2pi}{3}
ight)} = frac{1}{-frac{1}{2}} = -2$
Therefore, $secleft(frac{2pi}{3}
ight) = -2$.
Answer 3
Sophia Williams
To find $secleft(frac{2pi}{3}
ight)$, we need $cosleft(frac{2pi}{3}
ight)$.
Since $cosleft(frac{2pi}{3}
ight) = -frac{1}{2}$, we get:
$secleft(frac{2pi}{3}
ight) = frac{1}{-frac{1}{2}} = -2$
Hence, $secleft(frac{2pi}{3}
ight) = -2$.
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