What is the value of cos((5pi)/4+2pi) ?

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

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cos((5pi)/4+2pi)

cos (\frac{5 π}{4} + 2 π)

- \frac{2}{2}

Solution steps

cos (\frac{5 π}{4} + 2 π)

Simplify:

\frac{5 π}{4} + 2 π = \frac{13 π}{4}

= cos (\frac{13 π}{4})

cos (\frac{13 π}{4}) = cos (\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}

arctan (\frac{1.5}{2.5})

8 cos (29 0^{\circ})

cosh (0.0454 + i 0.357)

1 - 2 cos (\frac{π}{4})

arctan (1.32)

What is the value of cos((5pi)/4+2pi) ?
The value of cos((5pi)/4+2pi) is -(sqrt(2))/2