Find the secant of the angle when the point on the unit circle is at $ left(frac{sqrt{3}}{2}, frac{1}{2}
ight) $

Given the point $ \left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right) $ on the unit circle, we need to find the secant of the corresponding angle $ \theta $. Recall that $ \sec(\theta) = \frac{1}{\cos(\theta)} $ and $ \cos(\theta) $ is the x-coordinate.

So, $ \cos(\theta) = \frac{\sqrt{3}}{2} $. Hence,

$ \sec(\theta) = \frac{1}{\cos(\theta)} = \frac{1}{\frac{\sqrt{3}}{2}} = \frac{2}{\sqrt{3}} = \frac{2 \sqrt{3}}{3} $

Given the point $ left(frac{sqrt{3}}{2}, frac{1}{2}
ight) $ on the unit circle, the x-coordinate is $ cos( heta) = frac{sqrt{3}}{2} $. The secant function is the reciprocal of the cosine function:

$ sec( heta) = frac{2}{sqrt{3}} $

After rationalizing the denominator:

$ sec( heta) = frac{2 sqrt{3}}{3} $

Given the point $ left(frac{sqrt{3}}{2}, frac{1}{2}
ight) $, $ sec( heta) = frac{1}{cos( heta)} = frac{2}{sqrt{3}} $

So,

$ sec( heta) = frac{2 sqrt{3}}{3} $

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