What is the value of cos(-(7pi)/(12)) ?

The value of cos(-(7pi)/(12)) is (sqrt(2)(1-sqrt(3)))/4

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cos(-(7pi)/(12))

cos (- \frac{7 π}{12})

\frac{2 ( 1 - 3 )}{4}

Solution steps

cos (- \frac{7 π}{12})

Use the following property:

cos (- x) = cos (x)

cos (- \frac{7 π}{12}) = cos (\frac{7 π}{12})

= cos (\frac{7 π}{12})

Rewrite using trig identities:

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

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

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

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

Simplify

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

= \frac{2 ( 1 - 3 )}{4}

sin (π^{2})

cos (5 4^{\circ})

sin (\frac{15 π}{4})

cosh (ln (2))

4 cos (\frac{π}{4})

What is the value of cos(-(7pi)/(12)) ?
The value of cos(-(7pi)/(12)) is (sqrt(2)(1-sqrt(3)))/4