What is the value of sin(2pii) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(2pii)

sin (2 πi)

i \frac{- 1 + e ^{4 π}}{2 e ^{2 π}}

Solution steps

sin (2 πi)

Rewrite using trig identities:

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

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

Use the following trivial identity:

sin (0) = 0

Rewrite using trig identities:

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

Use the following trivial identity:

cos (0) = 1

Rewrite using trig identities:

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

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

Simplify

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

= i \frac{- 1 + e ^{4 π}}{2 e ^{2 π}}

cos (arccos (- 0.6))

1.5 \cdot sin (3 0^{\circ})

sin (\frac{1}{2} arcsin (- \frac{7}{25}))

cos (3 6^{\circ}) - cos (7 2^{\circ})

\frac{3500 sin ( 2 )}{sin ( 5 8 ^{\circ} )}

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