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

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

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cos(2pi-pi/4)

cos (2 π - \frac{π}{4})

\frac{2}{2}

Solution steps

cos (2 π - \frac{π}{4})

Rewrite using trig identities:

cos (0) cos (\frac{π}{4}) + sin (0) sin (\frac{π}{4})

= cos (0) cos (\frac{π}{4}) + sin (0) sin (\frac{π}{4})

Use the following trivial identity:

cos (0) = 1

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (0) = 0

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

= 1 \cdot \frac{2}{2} + 0 \cdot \frac{2}{2}

Simplify

= \frac{2}{2}

arcsin (0.9779)

3 sin (3 8^{\circ})

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arcsin (\frac{31 sin ( 2 0 ^{\circ} )}{12})