what is the exact value of $\displaystyle sec\frac{\pi}{4}$ ?

thanks

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- Mar 16th 2009, 01:17 AMjvignaciohelp with exact value.
what is the exact value of $\displaystyle sec\frac{\pi}{4}$ ?

thanks - Mar 16th 2009, 01:24 AMAir
$\displaystyle \sec \theta = \frac{1}{\cos \theta}$

$\displaystyle \therefore \sec \left(\frac{\pi}{4}\right) = \frac{1}{\cos \left(\frac{\pi}{4}\right)}$

We know that $\displaystyle \cos \frac{\pi}{4} = \frac{1}{\sqrt2}$

$\displaystyle \therefore \frac{1}{\left(\frac{1}{\sqrt2}\right)} = \sqrt2 = \sec \left(\frac{\pi}{4}\right) $