If the $sec( heta) = 2$ in the unit circle, find the angle $ heta$.
Answer 1
Abigail Nelson
Given $\sec(\theta) = 2$, we know $\sec(\theta) = \frac{1}{\cos(\theta)}$.
So, $\frac{1}{\cos(\theta)} = 2$ implies $\cos(\theta) = \frac{1}{2}$.
The cosine of $\theta$ is positive, so $\theta$ must be in the first or fourth quadrant.
Therefore, $\theta = \frac{\pi}{3}$ or $\theta = -\frac{\pi}{3}$.
Answer 2
Joseph Robinson
Given that $sec( heta) = 2$, we can find $ heta$ using the relationship $sec( heta) = frac{1}{cos( heta)}$.
Thus, $frac{1}{cos( heta)} = 2$ gives $cos( heta) = frac{1}{2}$.
In the unit circle, $cos( heta) = frac{1}{2}$ at $ heta = frac{pi}{3}$ or $ heta = 2pi – frac{pi}{3}$.
Therefore, $ heta = frac{pi}{3}$ or $ heta = frac{5pi}{3}$.
Answer 3
Alex Thompson
Given $sec( heta) = 2$, we have $sec( heta) = frac{1}{cos( heta)}$.
So, $cos( heta) = frac{1}{2}$.
Thus, $ heta = frac{pi}{3}$ or $ heta = frac{5pi}{3}$.
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