What is the value of cosh(i) ?

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Popular >

cosh(i)

cosh (i)

cos (1)

Decimal Notation

0.54030 \dots

Solution steps

cosh (i)

Use the Hyperbolic identity:

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

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

Simplify

\frac{e ^{i} + e ^{- i}}{2} : \frac{cos ( 1 ) + i sin ( 1 ) + cos ( - 1 ) + i sin ( - 1 )}{2}

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

e^{i} + e^{- i} = cos (1) + i sin (1) + cos (- 1) + i sin (- 1)

e^{i} + e^{- i}

Apply imaginary number rule:

e^{ia} = cos (a) + i sin (a)

= cos (1) + i sin (1) + e^{- i}

Apply imaginary number rule:

e^{ia} = cos (a) + i sin (a)

= cos (1) + i sin (1) + cos (- 1) + i sin (- 1)

= \frac{cos ( 1 ) + i sin ( 1 ) + cos ( - 1 ) + i sin ( - 1 )}{2}

= \frac{cos ( 1 ) + i sin ( 1 ) + cos ( - 1 ) + i sin ( - 1 )}{2}

Use the following property:

sin (- x) = - sin (x)

sin (- 1) = - sin (1)

= \frac{cos ( 1 ) + i sin ( 1 ) + cos ( - 1 ) + i ( - sin ( 1 ) )}{2}

Use the following property:

cos (- x) = cos (x)

cos (- 1) = cos (1)

= \frac{cos ( 1 ) + i sin ( 1 ) + cos ( 1 ) + i ( - sin ( 1 ) )}{2}

Simplify

= cos (1)

800 sin (6 0^{\circ})

tanh (4)

sin (2.5 π)

csc (\frac{7 π}{8})

e^{0} + sin (0)