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

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

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cos(-pi/8)

cos (- \frac{π}{8})

\frac{2 + 2}{2}

Solution steps

cos (- \frac{π}{8})

Use the following property:

cos (- x) = cos (x)

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

= cos (\frac{π}{8})

Rewrite using trig identities:

\frac{1 + cos ( \frac{π}{4} )}{2}

= \frac{1 + cos ( \frac{π}{4} )}{2}

Use the following trivial identity:

cos (\frac{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 (sin (- \frac{π}{6}))

tan (- 57 0^{\circ})

sin (arccos (- \frac{3}{5}))

tan (54 0^{\circ})

arccos (\frac{5}{5})

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