Find the value of $ sec( heta) $ for $ heta = frac{pi}{4} $ on the unit circle

To find the value of $ \sec(\theta) $ for $ \theta = \frac{\pi}{4} $ on the unit circle, we use the definition of secant, which is the reciprocal of cosine:

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

For $ \theta = \frac{\pi}{4} $, we have:

$ \cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2} $

Therefore:

$ \sec\left(\frac{\pi}{4}\right) = \frac{1}{\frac{\sqrt{2}}{2}} = \sqrt{2} $

To find the value of $ sec( heta) $ for $ heta = frac{pi}{4} $, we use:

$ sec( heta) = frac{1}{cos( heta)} $

For $ heta = frac{pi}{4} $:

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

So:

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

To find $ sec(frac{pi}{4}) $, use:

$ sec( heta) = frac{1}{cos( heta)} $

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

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

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