What is the value of cos(-(11pi)/(12)) ?

The value of cos(-(11pi)/(12)) is (-sqrt(6)-sqrt(2))/4

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cos(-(11pi)/(12))

cos (- \frac{11 π}{12})

\frac{- 6 - 2}{4}

Solution steps

cos (- \frac{11 π}{12})

Use the following property:

cos (- x) = cos (x)

cos (- \frac{11 π}{12}) = cos (\frac{11 π}{12})

= cos (\frac{11 π}{12})

Rewrite using trig identities:

cos (\frac{3 π}{4}) cos (\frac{π}{6}) - sin (\frac{3 π}{4}) sin (\frac{π}{6})

= cos (\frac{3 π}{4}) cos (\frac{π}{6}) - sin (\frac{3 π}{4}) sin (\frac{π}{6})

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

= (- \frac{2}{2}) \frac{3}{2} - \frac{2}{2} \cdot \frac{1}{2}

Simplify

(- \frac{2}{2}) \frac{3}{2} - \frac{2}{2} \cdot \frac{1}{2} : \frac{- 6 - 2}{4}

= \frac{- 6 - 2}{4}

arctan (\frac{4 3}{4})

sec (\frac{13 π}{4})

sinh (\frac{π}{2})

cos^{5} (π)

cot (3)

What is the value of cos(-(11pi)/(12)) ?
The value of cos(-(11pi)/(12)) is (-sqrt(6)-sqrt(2))/4