What is the value of cos(5/4 pi) ?

The value of cos(5/4 pi) is -(sqrt(2))/2

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cos(5/4 pi)

cos (\frac{5}{4} π)

- \frac{2}{2}

Solution steps

cos (\frac{5}{4} π)

Simplify:

\frac{5}{4} π = \frac{5 π}{4}

= cos (\frac{5 π}{4})

Rewrite using trig identities:

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

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

Use the following trivial identity:

cos (π) = (- 1)

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (π) = 0

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

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

Simplify

= - \frac{2}{2}

cot (4)

arctan (1.3)

cot (\frac{7 π}{2})

cos (\frac{π}{16})

sec (- \frac{π}{12})