What is the value of sin(i) ?

The value of sin(i) is i(-1+e^2)/(2e)

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sin(i)

sin (i)

i \frac{- 1 + e ^{2}}{2 e}

Solution steps

sin (i)

Rewrite using trig identities:

sin (0) cosh (1) + i cos (0) sinh (1)

= sin (0) cosh (1) + i cos (0) sinh (1)

Use the following trivial identity:

sin (0) = 0

Rewrite using trig identities:

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

Use the following trivial identity:

cos (0) = 1

Rewrite using trig identities:

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

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

Simplify

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

= i \frac{- 1 + e ^{2}}{2 e}

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