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受欢迎的三角函数 >

sinh(9)

解答

sinh (9)

解答

\frac{e ^{18} - 1}{2 e ^{9}}

+1

十进制

4051.54190 \dots

求解步骤

sinh (9)

使用双曲函数恒等式:

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

= \frac{e ^{9} - e ^{- 9}}{2}

\frac{e ^{9} - e ^{- 9}}{2} = \frac{e ^{18} - 1}{2 e ^{9}}

\frac{e ^{9} - e ^{- 9}}{2}

使用指数法则:

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

= \frac{e ^{9} - \frac{1}{e ^{9}}}{2}

化简

e^{9} - \frac{1}{e ^{9}} : \frac{e ^{18} - 1}{e ^{9}}

e^{9} - \frac{1}{e ^{9}}

将项转换为分式:

e^{9} = \frac{e ^{9} e ^{9}}{e ^{9}}

= \frac{e ^{9} e ^{9}}{e ^{9}} - \frac{1}{e ^{9}}

因为分母相等，所以合并分式:

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

= \frac{e ^{9} e ^{9} - 1}{e ^{9}}

e^{9} e^{9} - 1 = e^{18} - 1

e^{9} e^{9} - 1

e^{9} e^{9} = e^{18}

e^{9} e^{9}

使用指数法则:

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

e^{9} e^{9} = e^{9 + 9}

= e^{9 + 9}

数字相加:

9 + 9 = 18

= e^{18}

= e^{18} - 1

= \frac{e ^{18} - 1}{e ^{9}}

= \frac{\frac{e ^{18} - 1}{e ^{9}}}{2}

使用分式法则:

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

= \frac{e ^{18} - 1}{e ^{9} \cdot 2}

= \frac{e ^{18} - 1}{2 e ^{9}}

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