What is the value of sinh(-2) ?

The value of sinh(-2) is -(e^4-1)/(2e^2)

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sinh(-2)

sinh (- 2)

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

Decimal Notation

- 3.62686 \dots

Solution steps

sinh (- 2)

Use the following property:

sinh (- x) = - sinh (x)

sinh (- 2) = - sinh (2)

= - sinh (2)

Rewrite using trig identities:

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

sinh (2)

Use the Hyperbolic identity:

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

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

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

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

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

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

Join

e^{2} - \frac{1}{e ^{2}} : \frac{e ^{4} - 1}{e ^{2}}

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

Convert element to fraction:

e^{2} = \frac{e ^{2} e ^{2}}{e ^{2}}

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

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

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

e^{2} e^{2} - 1 = e^{4} - 1

e^{2} e^{2} - 1

e^{2} e^{2} = e^{4}

e^{2} e^{2}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{2} e^{2} = e^{2 + 2}

= e^{2 + 2}

Add the numbers:

2 + 2 = 4

= e^{4}

= e^{4} - 1

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

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

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

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

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

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

sec (\frac{3}{5})

2 + cos (π)

sin (6 0^{\circ}) + cos (6 0^{\circ})

cos (1 5^{\circ}) cos (3 0^{\circ}) - sin (1 5^{\circ}) sin (3 0^{\circ})

cos (4 \cdot π)