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How do you find sec pi/4 in terms of radians?

1 Answer

Aug 8, 2015

$sec (\frac{π}{4}) = \sqrt{2}$ $sec(pi/4) = sqrt(2)$
Note, however, that $\sqrt{2}$ $sqrt(2)$ is not in radians. It is a ratio (not in degrees or radians); the argument of $sec$ $sec$ (namely $\frac{π}{4}$ $pi/4$ ) is the component in radians

Explanation:

$sec (\frac{π}{4})$ $sec(pi/4)$

$XXXX$ $color(white)("XXXX")$ $= \frac{1}{cos (\frac{π}{4})}$ $=1/cos(pi/4)$

$\frac{π}{4}$ $pi/4$ radians is one of the standard angles with $cos (\frac{π}{4}) = \frac{1}{\sqrt{2}}$ $cos(pi/4) = 1/sqrt(2)$

So $sec (\frac{π}{4}) = \frac{1}{\frac{1}{\sqrt{2}}} = \sqrt{2}$ $sec(pi/4) = 1/(1/sqrt(2)) = sqrt(2)$

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