What is the value of cos(17/12 pi) ?

The value of cos(17/12 pi) is (sqrt(2)-sqrt(6))/4

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cos(17/12 pi)

cos (\frac{17}{12} π)

\frac{2 - 6}{4}

Solution steps

cos (\frac{17}{12} π)

Simplify:

\frac{17}{12} π = \frac{17 π}{12}

= cos (\frac{17 π}{12})

Rewrite using trig identities:

cos (\frac{3 π}{4}) cos (\frac{2 π}{3}) - sin (\frac{3 π}{4}) sin (\frac{2 π}{3})

= cos (\frac{3 π}{4}) cos (\frac{2 π}{3}) - sin (\frac{3 π}{4}) sin (\frac{2 π}{3})

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

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

Simplify

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

= \frac{2 - 6}{4}

arcsin (\frac{2}{5})

tan (arcsin (\frac{3}{4}) - arccos (\frac{1}{3}))

sin (15 6^{\circ})

\frac{sin ( 1 )}{1 - sin ( 1 )}

52 cos (\frac{π}{4})

What is the value of cos(17/12 pi) ?
The value of cos(17/12 pi) is (sqrt(2)-sqrt(6))/4