# Thread: help with exact value.

1. ## help with exact value.

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

thanks

2. 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 $\cos \frac{\pi}{4} = \frac{1}{\sqrt2}$

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