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

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

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cos(pi/(16))

cos (\frac{π}{16})

\frac{2 + 2 + 2}{2}

Solution steps

cos (\frac{π}{16})

Rewrite using trig identities:

\frac{1 + cos ( \frac{π}{8} )}{2}

= \frac{1 + cos ( \frac{π}{8} )}{2}

Rewrite using trig identities:

cos (\frac{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}

sec (- \frac{π}{12})

cos (\frac{3}{2})

sin (arcsin (\frac{3}{2}))

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

5 cos (7 0^{\circ})

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