What is the value of cos((23pi)/4) ?

The value of cos((23pi)/4) is (sqrt(2))/2

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cos((23pi)/4)

cos (\frac{23 π}{4})

\frac{2}{2}

Solution steps

cos (\frac{23 π}{4})

cos (\frac{23 π}{4}) = cos (\frac{7 π}{4})

= cos (\frac{7 π}{4})

Rewrite using trig identities:

cos (π) cos (\frac{3 π}{4}) - sin (π) sin (\frac{3 π}{4})

= cos (π) cos (\frac{3 π}{4}) - sin (π) sin (\frac{3 π}{4})

Use the following trivial identity:

cos (π) = (- 1)

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

Use the following trivial identity:

sin (π) = 0

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

= (- 1) (- \frac{2}{2}) - 0 \cdot \frac{2}{2}

Simplify

= \frac{2}{2}

sin (14 5^{\circ})

tan (\frac{- 11 π}{6})

\frac{1}{cos ( 3 3 ^{\circ} ) cos ( 1 2 ^{\circ} ) - sin ( 3 3 ^{\circ} ) sin ( 1 2 ^{\circ} )}

arcsin (\frac{19}{32})

arcsin (cos (\frac{π}{2}))