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受欢迎的三角函数 >

sinh(6)

解答

sinh (6)

解答

\frac{e ^{12} - 1}{2 e ^{6}}

+1

十进制

201.71315 \dots

求解步骤

sinh (6)

使用双曲函数恒等式:

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

= \frac{e ^{6} - e ^{- 6}}{2}

\frac{e ^{6} - e ^{- 6}}{2} = \frac{e ^{12} - 1}{2 e ^{6}}

\frac{e ^{6} - e ^{- 6}}{2}

使用指数法则:

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

= \frac{e ^{6} - \frac{1}{e ^{6}}}{2}

化简

e^{6} - \frac{1}{e ^{6}} : \frac{e ^{12} - 1}{e ^{6}}

e^{6} - \frac{1}{e ^{6}}

将项转换为分式:

e^{6} = \frac{e ^{6} e ^{6}}{e ^{6}}

= \frac{e ^{6} e ^{6}}{e ^{6}} - \frac{1}{e ^{6}}

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 ^{6} e ^{6} - 1}{e ^{6}}

e^{6} e^{6} - 1 = e^{12} - 1

e^{6} e^{6} - 1

e^{6} e^{6} = e^{12}

e^{6} e^{6}

使用指数法则:

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

e^{6} e^{6} = e^{6 + 6}

= e^{6 + 6}

数字相加:

6 + 6 = 12

= e^{12}

= e^{12} - 1

= \frac{e ^{12} - 1}{e ^{6}}

= \frac{\frac{e ^{12} - 1}{e ^{6}}}{2}

使用分式法则:

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

= \frac{e ^{12} - 1}{e ^{6} \cdot 2}

= \frac{e ^{12} - 1}{2 e ^{6}}

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