What is the value of cos((5pi)/(16)) ?

The value of cos((5pi)/(16)) is (sqrt(2-\sqrt{2-\sqrt{2)}})/2

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cos((5pi)/(16))

cos (\frac{5 π}{16})

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

Solution steps

cos (\frac{5 π}{16})

Rewrite using trig identities:

\frac{1 + cos ( \frac{5 π}{8} )}{2}

= \frac{1 + cos ( \frac{5 π}{8} )}{2}

Rewrite using trig identities:

cos (\frac{5 π}{8}) = - \frac{2 - 2}{2}

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

Simplify

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

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

cos (arcsin (- \frac{2}{5}))

arcsin (0.52)

3 cos (34 0^{\circ})

4 sin^{2} (\frac{π}{4}) + 49 cos^{2} (\frac{π}{4})

sin (\frac{6 π}{6})

What is the value of cos((5pi)/(16)) ?
The value of cos((5pi)/(16)) is (sqrt(2-\sqrt{2-\sqrt{2)}})/2