What is the value of sin(2i) ?

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

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sin(2i)

sin (2 i)

i \frac{- 1 + e ^{4}}{2 e ^{2}}

Solution steps

sin (2 i)

Rewrite using trig identities:

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

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

Use the following trivial identity:

sin (0) = 0

Rewrite using trig identities:

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

Use the following trivial identity:

cos (0) = 1

Rewrite using trig identities:

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

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

Simplify

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

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

cos (\frac{5}{13} + \frac{3}{5})

arccos (0.37)

arccos (0.52)

cosh (ln (8))

\frac{24}{cos ( 2 0 ^{\circ} )}