What is the value of cos((31pi)/4) ?

The value of cos((31pi)/4) is (sqrt(2))/2

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cos((31pi)/4)

cos (\frac{31 π}{4})

\frac{2}{2}

Solution steps

cos (\frac{31 π}{4})

cos (\frac{31 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}

1 - 2 sin^{2} (1 0^{\circ})

25 \cdot cos (5 4^{\circ})

\frac{1}{csc ( 3 0 ^{\circ} )}

tan (- 84 0^{\circ})

sin (2 arctan (2))