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受欢迎的三角函数 >

arctanh(1/3)

解答

arctanh (\frac{1}{3})

解答

\frac{ln ( 2 )}{2}

+1

十进制

0.34657 \dots

求解步骤

arctanh (\frac{1}{3})

使用双曲函数恒等式:

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

= \frac{ln ( \frac{1 + \frac{1}{3}}{1 - \frac{1}{3}} )}{2}

\frac{ln ( \frac{1 + \frac{1}{3}}{1 - \frac{1}{3}} )}{2} = \frac{ln ( 2 )}{2}

\frac{ln ( \frac{1 + \frac{1}{3}}{1 - \frac{1}{3}} )}{2}

\frac{1 + \frac{1}{3}}{1 - \frac{1}{3}} = 2

\frac{1 + \frac{1}{3}}{1 - \frac{1}{3}}

化简

1 - \frac{1}{3} : \frac{2}{3}

1 - \frac{1}{3}

将项转换为分式:

1 = \frac{1 \cdot 3}{3}

= \frac{1 \cdot 3}{3} - \frac{1}{3}

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 3 - 1}{3}

1 \cdot 3 - 1 = 2

1 \cdot 3 - 1

数字相乘:

1 \cdot 3 = 3

= 3 - 1

数字相减:

3 - 1 = 2

= 2

= \frac{2}{3}

= \frac{1 + \frac{1}{3}}{\frac{2}{3}}

化简

1 + \frac{1}{3} : \frac{4}{3}

1 + \frac{1}{3}

将项转换为分式:

1 = \frac{1 \cdot 3}{3}

= \frac{1 \cdot 3}{3} + \frac{1}{3}

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 3 + 1}{3}

1 \cdot 3 + 1 = 4

1 \cdot 3 + 1

数字相乘:

1 \cdot 3 = 3

= 3 + 1

数字相加:

3 + 1 = 4

= 4

= \frac{4}{3}

= \frac{\frac{4}{3}}{\frac{2}{3}}

分式相除:

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

= \frac{4 \cdot 3}{3 \cdot 2}

约分:

3

= \frac{4}{2}

数字相除:

\frac{4}{2} = 2

= 2

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

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

流行的例子

sin (2 x) = tan (x)

cos (x) = 0.35

sin (\frac{17 π}{6})

cos (2 θ) = \frac{1}{2}

tan(arcsin(-4/5))

tan (arcsin (- \frac{4}{5}))