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

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

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cos((17pi)/(12))

cos (\frac{17 π}{12})

\frac{2 - 6}{4}

Solution steps

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}

sin^{2} (2 π)

arccot (3)

- cos (0)

cos (6 0^{\circ} - 4 5^{\circ})

sin (2 π)

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