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})

Use the following property:

cos (- x) = cos (x)

cos (- \frac{17 π}{12}) = cos (\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}

- 5 cos (1)

- 5 cos (3)

π - arctan (\frac{1}{2})

arctan (\frac{14}{11})

arctan (\frac{7}{13})

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