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

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

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cos(5 pi/4)

cos (5 \frac{π}{4})

- \frac{2}{2}

Solution steps

cos (5 \cdot \frac{π}{4})

Simplify:

5 \cdot \frac{π}{4} = \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}

tan^{2} (\frac{11 π}{12})

arccos (- \frac{1}{9})

tan (20 5^{\circ})

(sin (6 0^{\circ})) (cos (3 0^{\circ})) + tan (4 5^{\circ})

sec (\frac{7 π}{6}) - cot (\frac{5 π}{6})