Find the value of $sec( heta)$ if point $P(frac{1}{2}, frac{sqrt{3}}{2})$ lies on the unit circle.
Answer 1
Emily Hall
To find $\sec(\theta)$, we need to know $\cos(\theta)$. Given the coordinates on the unit circle, $\cos(\theta) = x$-coordinate of point $P$.
Here, $x = \frac{1}{2}$. Therefore, $\cos(\theta) = \frac{1}{2}$.
Recall that $\sec(\theta) = \frac{1}{\cos(\theta)}$.
Thus, $\sec(\theta) = \frac{1}{\frac{1}{2}} = 2$.
Therefore, $\sec(\theta) = 2$.
Answer 2
Thomas Walker
Given the point $P(frac{1}{2}, frac{sqrt{3}}{2})$ on the unit circle, we can determine $sec( heta)$ by first finding $cos( heta)$, which is the x-coordinate of $P$.
We have $cos( heta) = frac{1}{2}$.
Since $sec( heta) = frac{1}{cos( heta)}$, we find:
$ sec( heta) = frac{1}{frac{1}{2}} = 2 $
Thus, $sec( heta) = 2$.
Answer 3
Christopher Garcia
Given point $P(frac{1}{2}, frac{sqrt{3}}{2})$ on the unit circle, $cos( heta) = frac{1}{2}$.
So, $sec( heta) = frac{1}{cos( heta)} = frac{1}{frac{1}{2}} = 2$.
Thus, $sec( heta) = 2$.
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