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

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

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cos((5pi)/4)

cos (\frac{5 π}{4})

- \frac{2}{2}

Solution steps

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}

cos^{2} (\frac{π}{2})

arcsin (\frac{3}{2})

cos^{2} (x) - sin^{2} (x) = 1 - 2 sin^{2} (x)

sin (24 0^{\circ})

cos (\frac{7 π}{3})