How do you find the exact value of $cos [\frac{- 7 π}{6}]$ $cos [(-7pi)/6]$ ?

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How do you find the exact value of $cos [\frac{- 7 π}{6}]$ $cos [(-7pi)/6]$ ?

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Answer 1 · 2015-04-21T22:05:25

$cos (\frac{- 7 π}{6}) = - (\frac{\sqrt{3}}{2})$ $cos((-7pi)/(6))=-(sqrt(3)/2)$

First step $cos (- \frac{7}{6} π) = cos (\frac{7}{6} π)$ $cos(-7/6pi)=cos(7/6pi)$ because cosine is an even function (for evry $x$ $x$ $f (- x) = f (x)$ $f(-x)=f(x)$ )

Now you have to reduce $cos (\frac{7}{6} π)$ $cos(7/6 pi)$ to a value of a functon of an angle smaller than $\frac{π}{2}$ $pi/2$ $r a d$ $rad$ . To do this you use the formula
$cos (π + x) = - cos (x)$ $cos(pi+x)= - cos(x)$ . So you get $cos (\frac{7}{6} π) = - cos (\frac{π}{6}) = - \frac{\sqrt{3}}{2}$ $cos(7/6 pi)=-cos(pi/6)=-(sqrt(3))/2$

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How do you find the exact value of $cos [\frac{- 7 π}{6}]$ $cos [(-7pi)/6]$ ?

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