help with exact value.

**jvignacio** · March 16th 2009, 01:17 AM

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

thanks

**Air** · March 16th 2009, 01:24 AM

Originally Posted by jvignacio

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

thanks

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

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

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

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

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