What is the value of cos(-(3pi)/8) ?

The value of cos(-(3pi)/8) is (sqrt(2-\sqrt{2)})/2

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cos(-(3pi)/8)

cos (- \frac{3 π}{8})

\frac{2 - 2}{2}

Solution steps

cos (- \frac{3 π}{8})

Use the following property:

cos (- x) = cos (x)

cos (- \frac{3 π}{8}) = cos (\frac{3 π}{8})

= cos (\frac{3 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}

csc (arccos (\frac{7}{4}))

6 sin (\frac{2 π}{3})

4 sec (2 π)

cos^{3} (1)

\frac{tan ( 5 ^{\circ} ) + tan ( 2 5 ^{\circ} )}{1 - tan ( 5 ^{\circ} ) tan ( 2 5 ^{\circ} )}

What is the value of cos(-(3pi)/8) ?
The value of cos(-(3pi)/8) is (sqrt(2-\sqrt{2)})/2