What is the value of sinh(ipi) ?

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sinh(ipi)

sinh (iπ)

0

Solution steps

sinh (iπ)

Use the Hyperbolic identity:

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

= \frac{e ^{πi} - e ^{- πi}}{2}

\frac{e ^{πi} - e ^{- πi}}{2} = 0

\frac{e ^{πi} - e ^{- πi}}{2}

e^{πi} - e^{- πi} = 0

e^{πi} - e^{- πi}

Apply imaginary number rule:

e^{iπ} = - 1

= - 1 - e^{- πi}

e^{- πi} = - 1

e^{- πi}

Apply imaginary number rule:

e^{iaπ} = (- 1)^{a}

= (- 1)^{- 1}

Apply exponent rule:

(- a)^{n} = - a^{n},

n

is odd

(- 1)^{- 1} = - 1^{- 1}

= - 1^{- 1}

Apply rule

1^{a} = 1

= - 1

= - 1 - (- 1)

Apply rule

- (- a) = a

= - 1 + 1

Add/Subtract the numbers:

- 1 + 1 = 0

= 0

= \frac{0}{2}

Apply rule

\frac{0}{a} = 0, a \neq = 0

= 0

= 0

10 + 4 cos (2 \cdot 0.31616)

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tan (arcsin (\frac{1}{2}))

sin (2 (\frac{3 π}{4}))