What is the value of cos(-22.5) ?

The value of cos(-22.5) is (sqrt(2+\sqrt{2)})/2

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cos(-22.5)

cos (- 22. 5^{\circ})

\frac{2 + 2}{2}

Solution steps

cos (- 22. 5^{\circ})

Use the following property:

cos (- x) = cos (x)

cos (- 22. 5^{\circ}) = cos (22. 5^{\circ})

= cos (22. 5^{\circ})

Rewrite using trig identities:

\frac{1 + cos ( 4 5 ^{\circ} )}{2}

= \frac{1 + cos ( 4 5 ^{\circ} )}{2}

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

= \frac{1 + \frac{2}{2}}{2}

Simplify

\frac{1 + \frac{2}{2}}{2} : \frac{2 + 2}{2}

= \frac{2 + 2}{2}

cos (2 \cdot \frac{3 π}{4})

\frac{2 tan ( \frac{5 π}{6} )}{1 - tan ^{2} ( \frac{5 π}{6} )}

cos (- \frac{7 π}{3})

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

arccos (0.77)

What is the value of cos(-22.5) ?
The value of cos(-22.5) is (sqrt(2+\sqrt{2)})/2