How do I find the value of sec 225?

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Answer 1 · 2015-09-17T14:12:43

$sec225 = -sqrt2$

First thing we do is remember that $secx = 1/cosx$ , so

$sec225 = 1/cos225$

Then we see that we can rewrite 225 as $180 + 45$ , so

$sec225 = 1/cos(180+45)$

Using the formula $cos(a+b) = cos(a)cos(b) - sin(a)sin(b)$ we have that

$cos225 = cos(180)cos(45) - sin(180)sin(45)$

From looking at the unit circle we know that $cos(180) = -1$ and that $sin(180) = 0$ , so

$cos225 = (-1)cos(45) - 0sin(45)$
$cos225 = -cos45$

We know that $cos(45) = sqrt2/2$ , so

$cos225 = -sqrt2/2$
Therefore the secant is

$sec225 = 1/cos225 = -2/sqrt2$

Rationalizing,

$sec225 = -2sqrt2/2$

And finally we cancel that pesky 2

$sec225 = -sqrt2$