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受欢迎的三角函数 >

arctanh(0.98)

解答

arctanh (0.98)

解答

\frac{ln ( 99 )}{2}

+1

十进制

2.29755 \dots

求解步骤

arctanh (0.98)

= arctanh (\frac{49}{50})

使用三角恒等式改写:

\frac{ln ( 99 )}{2}

arctanh (\frac{49}{50})

使用双曲函数恒等式:

arctanh (x) = \frac{ln ( \frac{1 + x}{1 - x} )}{2}

= \frac{ln ( \frac{1 + \frac{49}{50}}{1 - \frac{49}{50}} )}{2}

\frac{ln ( \frac{1 + \frac{49}{50}}{1 - \frac{49}{50}} )}{2} = \frac{ln ( 99 )}{2}

\frac{ln ( \frac{1 + \frac{49}{50}}{1 - \frac{49}{50}} )}{2}

\frac{1 + \frac{49}{50}}{1 - \frac{49}{50}} = 99

\frac{1 + \frac{49}{50}}{1 - \frac{49}{50}}

化简

1 - \frac{49}{50} : \frac{1}{50}

1 - \frac{49}{50}

将项转换为分式:

1 = \frac{1 \cdot 50}{50}

= \frac{1 \cdot 50}{50} - \frac{49}{50}

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{1 \cdot 50 - 49}{50}

1 \cdot 50 - 49 = 1

1 \cdot 50 - 49

数字相乘:

1 \cdot 50 = 50

= 50 - 49

数字相减:

50 - 49 = 1

= 1

= \frac{1}{50}

= \frac{1 + \frac{49}{50}}{\frac{1}{50}}

化简

1 + \frac{49}{50} : \frac{99}{50}

1 + \frac{49}{50}

将项转换为分式:

1 = \frac{1 \cdot 50}{50}

= \frac{1 \cdot 50}{50} + \frac{49}{50}

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{1 \cdot 50 + 49}{50}

1 \cdot 50 + 49 = 99

1 \cdot 50 + 49

数字相乘:

1 \cdot 50 = 50

= 50 + 49

数字相加:

50 + 49 = 99

= 99

= \frac{99}{50}

= \frac{\frac{99}{50}}{\frac{1}{50}}

分式相除:

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

= \frac{99 \cdot 50}{50 \cdot 1}

整理后得

= \frac{99 \cdot 50}{50}

约分:

50

= 99

= \frac{ln ( 99 )}{2}

= \frac{ln ( 99 )}{2}

= \frac{ln ( 99 )}{2}

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cos (3 0^{\circ}) 100

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9.8 \cdot sin (3 5^{\circ})

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