What is the value of cos(27/8 pi) ?

The value of cos(27/8 pi) is -(sqrt(2-\sqrt{2)})/2

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cos(27/8 pi)

cos (\frac{27}{8} π)

- \frac{2 - 2}{2}

Solution steps

cos (\frac{27}{8} π)

Simplify:

\frac{27}{8} π = \frac{27 π}{8}

= cos (\frac{27 π}{8})

cos (\frac{27 π}{8}) = cos (\frac{11 π}{8})

= 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}

\frac{28}{cos ( 4 5 ^{\circ} )}

arctan (\frac{9}{23})

sec (π) \cdot tan (π)

cot (\frac{7}{4})

arcsin (csc (- \frac{π}{2}))

What is the value of cos(27/8 pi) ?
The value of cos(27/8 pi) is -(sqrt(2-\sqrt{2)})/2