Find the value of $ sec(θ) $ at $ θ = frac{pi}{3} $ on the unit circle

To find the value of $ \sec(θ) $ at $ θ = \frac{\pi}{3} $ on the unit circle, we first find the cosine of the angle:

$ \cos\left(\frac{\pi}{3}\right) = \frac{1}{2} $

Then, since $ \sec(θ) $ is the reciprocal of $ \cos(θ) $:

$ \sec\left(\frac{\pi}{3}\right) = \frac{1}{\cos\left(\frac{\pi}{3}\right)} = \frac{1}{\frac{1}{2}} = 2 $

To determine $ secleft(frac{pi}{4}
ight) $ using the unit circle, find the cosine of the angle:

$ cosleft(frac{pi}{4}
ight) = frac{sqrt{2}}{2} $

The secant is the reciprocal of cosine:

$ secleft(frac{pi}{4}
ight) = frac{1}{cosleft(frac{pi}{4}
ight)} = frac{1}{frac{sqrt{2}}{2}} = sqrt{2} $

To calculate $ sec(0) $ on the unit circle, note that:

$ cos(0) = 1 $

So:

$ sec(0) = frac{1}{1} = 1 $

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