Find the value of $ sec( heta) $ when $ heta = frac{pi}{4} $ on the unit circle.
Answer 1
Abigail Nelson
To find the value of $ \sec(\theta) $ when $ \theta = \frac{\pi}{4} $ on the unit circle, we first recall that $ \sec(\theta) = \frac{1}{\cos(\theta)} $.
At $ \theta = \frac{\pi}{4} $, the cosine of $ \theta $ is $ \cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2} $.
Therefore,
$ \sec(\frac{\pi}{4}) = \frac{1}{\cos(\frac{\pi}{4})} = \frac{1}{\frac{\sqrt{2}}{2}} = \frac{2}{\sqrt{2}} = \sqrt{2} $
Answer 2
Thomas Walker
To determine $ sec( heta) $ for $ heta = frac{pi}{4} $ on the unit circle, note that $ sec( heta) = frac{1}{cos( heta)} $.
We know that $ cos(frac{pi}{4}) = frac{sqrt{2}}{2} $.
Thus,
$ sec(frac{pi}{4}) = frac{1}{frac{sqrt{2}}{2}} = frac{2}{sqrt{2}} = sqrt{2} $
Answer 3
Christopher Garcia
Given $ heta = frac{pi}{4} $, we use $ sec( heta) = frac{1}{cos( heta)} $.
With $ cos(frac{pi}{4}) = frac{sqrt{2}}{2} $, we get
$ sec(frac{pi}{4}) = sqrt{2} $
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