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受欢迎的三角函数 >

sinh(7/20)

解答

sinh (\frac{7}{20})

解答

\frac{e ^{\frac{7}{10}} - 1}{2 e ^{\frac{7}{20}}}

+1

十进制

0.35718 \dots

求解步骤

sinh (\frac{7}{20})

使用双曲函数恒等式:

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

= \frac{e ^{\frac{7}{20}} - e ^{- \frac{7}{20}}}{2}

\frac{e ^{\frac{7}{20}} - e ^{- \frac{7}{20}}}{2} = \frac{e ^{\frac{7}{10}} - 1}{2 e ^{\frac{7}{20}}}

\frac{e ^{\frac{7}{20}} - e ^{- \frac{7}{20}}}{2}

使用指数法则:

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

= \frac{e ^{\frac{7}{20}} - \frac{1}{e ^{\frac{7}{20}}}}{2}

化简

e^{\frac{7}{20}} - \frac{1}{e ^{\frac{7}{20}}} : \frac{e ^{\frac{7}{10}} - 1}{e ^{\frac{7}{20}}}

e^{\frac{7}{20}} - \frac{1}{e ^{\frac{7}{20}}}

将项转换为分式:

e^{\frac{7}{20}} = \frac{e ^{\frac{7}{20}} e ^{\frac{7}{20}}}{e ^{\frac{7}{20}}}

= \frac{e ^{\frac{7}{20}} e ^{\frac{7}{20}}}{e ^{\frac{7}{20}}} - \frac{1}{e ^{\frac{7}{20}}}

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 ^{\frac{7}{20}} e ^{\frac{7}{20}} - 1}{e ^{\frac{7}{20}}}

e^{\frac{7}{20}} e^{\frac{7}{20}} - 1 = e^{2 \cdot \frac{7}{20}} - 1

e^{\frac{7}{20}} e^{\frac{7}{20}} - 1

e^{\frac{7}{20}} e^{\frac{7}{20}} = e^{2 \cdot \frac{7}{20}}

e^{\frac{7}{20}} e^{\frac{7}{20}}

使用指数法则:

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

e^{\frac{7}{20}} e^{\frac{7}{20}} = e^{\frac{7}{20} + \frac{7}{20}}

= e^{\frac{7}{20} + \frac{7}{20}}

同类项相加:

\frac{7}{20} + \frac{7}{20} = 2 \cdot \frac{7}{20}

= e^{2 \cdot \frac{7}{20}}

= e^{2 \cdot \frac{7}{20}} - 1

= \frac{e ^{2 \cdot \frac{7}{20}} - 1}{e ^{\frac{7}{20}}}

乘

2 \cdot \frac{7}{20} : \frac{7}{10}

2 \cdot \frac{7}{20}

分式相乘:

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

= \frac{7 \cdot 2}{20}

数字相乘:

7 \cdot 2 = 14

= \frac{14}{20}

约分:

2

= \frac{7}{10}

= \frac{e ^{\frac{7}{10}} - 1}{e ^{\frac{7}{20}}}

= \frac{\frac{e ^{\frac{7}{10}} - 1}{e ^{\frac{7}{20}}}}{2}

使用分式法则:

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

= \frac{e ^{\frac{7}{10}} - 1}{e ^{\frac{7}{20}} \cdot 2}

= \frac{e ^{\frac{7}{10}} - 1}{2 e ^{\frac{7}{20}}}

流行的例子

sin(45)+tan(30)

sin (4 5^{\circ}) + tan (3 0^{\circ})

csc (4 7^{\circ})

arctan (\frac{3}{12})

arctan (\frac{3}{11})

cot (\frac{π}{16})