What is the value of sinh(ln(5)) ?

The value of sinh(ln(5)) is 12/5

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sinh(ln(5))

sinh (ln (5))

\frac{12}{5}

Decimal Notation

2.4

Solution steps

sinh (ln (5))

Use the Hyperbolic identity:

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

= \frac{e ^{l n (5)} - e ^{- l n (5)}}{2}

\frac{e ^{l n (5)} - e ^{- l n (5)}}{2} = \frac{12}{5}

\frac{e ^{l n (5)} - e ^{- l n (5)}}{2}

e^{l n (5)} = 5

e^{l n (5)}

Apply log rule:

a^{l o g_{a} (b)} = b

= 5

e^{- l n (5)} = 5^{- 1}

e^{- l n (5)}

Apply exponent rule:

a^{b c} = (a^{b})^{c}

= (e^{l n (5)})^{- 1}

Apply log rule:

a^{l o g_{a} (b)} = b

e^{l n (5)} = 5

= 5^{- 1}

= \frac{5 - 5 ^{- 1}}{2}

Simplify

\frac{5 - 5 ^{- 1}}{2}

Apply exponent rule:

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

= \frac{5 - \frac{1}{5}}{2}

Join

5 - \frac{1}{5} : \frac{24}{5}

5 - \frac{1}{5}

Convert element to fraction:

5 = \frac{5 \cdot 5}{5}

= \frac{5 \cdot 5}{5} - \frac{1}{5}

Since the denominators are equal, combine the fractions:

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

= \frac{5 \cdot 5 - 1}{5}

5 \cdot 5 - 1 = 24

5 \cdot 5 - 1

Multiply the numbers:

5 \cdot 5 = 25

= 25 - 1

Subtract the numbers:

25 - 1 = 24

= 24

= \frac{24}{5}

= \frac{\frac{24}{5}}{2}

Apply the fraction rule:

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

= \frac{24}{5 \cdot 2}

Multiply the numbers:

5 \cdot 2 = 10

= \frac{24}{10}

Cancel the common factor:

2

= \frac{12}{5}

= \frac{12}{5}

= \frac{12}{5}

cos (arcsin (\frac{1}{4}))

20 \cdot cos (3 0^{\circ})

tan (6 π)

cos^{2} (7 0^{\circ})

sin (\frac{5}{3} π)