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How do you find the exact values $cos (\frac{π}{4})$ $cos (pi/4)$ using the special triangles?

1 Answer

Aug 4, 2015

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

Explanation:

The "special triangle" corresponding to $\frac{π}{4}$ $pi/4$ is an isosceles triangle with equal adjacent and opposite sides (and a hypotenuse that can be calculated using the Pythagorean Theorem).

By definition
$XXXX$ $color(white)("XXXX")$ $cos = \frac{adjacent}{hypontenuse}$ $cos = ("adjacent")/("hypontenuse")$
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