What is the value of cos(2pii) ?

The value of cos(2pii) is (e^{4pi}+1)/(2e^{2pi)}

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cos(2pii)

cos (2 πi)

\frac{e ^{4 π} + 1}{2 e ^{2 π}}

Solution steps

cos (2 πi)

Rewrite using trig identities:

cos (0) cosh (2 π) - i sin (0) sinh (2 π)

= cos (0) cosh (2 π) - i sin (0) sinh (2 π)

Use the following trivial identity:

cos (0) = 1

Rewrite using trig identities:

cosh (2 π) = \frac{e ^{4 π} + 1}{2 e ^{2 π}}

Use the following trivial identity:

sin (0) = 0

Rewrite using trig identities:

sinh (2 π) = \frac{e ^{4 π} - 1}{2 e ^{2 π}}

= 1 \cdot \frac{e ^{4 π} + 1}{2 e ^{2 π}} - i 0 \cdot \frac{e ^{4 π} - 1}{2 e ^{2 π}}

Simplify

1 \cdot \frac{e ^{4 π} + 1}{2 e ^{2 π}} - i 0 \cdot \frac{e ^{4 π} - 1}{2 e ^{2 π}} : \frac{e ^{4 π} + 1}{2 e ^{2 π}}

= \frac{e ^{4 π} + 1}{2 e ^{2 π}}

cos (- 1 (\frac{5}{7}))

tan (\frac{3}{2} π)

cot (4 7^{\circ})

\frac{tan ( 5 0 ^{\circ} ) - tan ( 2 0 ^{\circ} )}{1 + tan ( 5 0 ^{\circ} ) tan ( 2 0 ^{\circ} )}

What is the value of cos(2pii) ?
The value of cos(2pii) is (e^{4pi}+1)/(2e^{2pi)}