What is the value of cos((11pi)/8) ?

The value of cos((11pi)/8) is -(sqrt(2-\sqrt{2)})/2

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cos((11pi)/8)

cos (\frac{11 π}{8})

- \frac{2 - 2}{2}

Solution steps

cos (\frac{11 π}{8})

Rewrite using trig identities:

- \frac{1 + cos ( \frac{3 π}{4} )}{2}

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

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

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

Simplify

- \frac{1 - \frac{2}{2}}{2} : - \frac{2 - 2}{2}

= - \frac{2 - 2}{2}

arccos (cos (\frac{42 π}{53}))

100 cos (6 0^{\circ})

cos (2 arctan (\frac{4}{3}))

cos^{2} (- 1)

arctan (0.36)

What is the value of cos((11pi)/8) ?
The value of cos((11pi)/8) is -(sqrt(2-\sqrt{2)})/2