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受欢迎的三角函数 >

arcsinh(0.5)

解答

arcsinh (0.5)

解答

ln (\frac{1 + 5}{2})

+1

十进制

0.48121 \dots

求解步骤

arcsinh (0.5)

= arcsinh (\frac{1}{2})

使用三角恒等式改写:

ln (\frac{1 + 5}{2})

arcsinh (\frac{1}{2})

使用双曲函数恒等式:

arcsinh (x) = ln (x + x^{2} + 1)

= ln \frac{1}{2} + (\frac{1}{2})^{2} + 1

ln \frac{1}{2} + (\frac{1}{2})^{2} + 1 = ln (\frac{1 + 5}{2})

ln \frac{1}{2} + (\frac{1}{2})^{2} + 1

(\frac{1}{2})^{2} + 1 = \frac{5}{2}

(\frac{1}{2})^{2} + 1

(\frac{1}{2})^{2} = \frac{1}{4}

(\frac{1}{2})^{2}

使用指数法则:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{2}}{2 ^{2}}

使用法则

1^{a} = 1

1^{2} = 1

= \frac{1}{2 ^{2}}

2^{2} = 4

= \frac{1}{4}

= \frac{1}{4} + 1

化简

\frac{1}{4} + 1 : \frac{5}{4}

\frac{1}{4} + 1

将项转换为分式:

1 = \frac{1 \cdot 4}{4}

= \frac{1}{4} + \frac{1 \cdot 4}{4}

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 + 1 \cdot 4}{4}

1 + 1 \cdot 4 = 5

1 + 1 \cdot 4

数字相乘:

1 \cdot 4 = 4

= 1 + 4

数字相加:

1 + 4 = 5

= 5

= \frac{5}{4}

= \frac{5}{4}

使用根式运算法则:

n \frac{a}{b} = \frac{n a}{n b},

假定

a \geq 0, b \geq 0

= \frac{5}{4}

4 = 2

4

因式分解数字:

4 = 2^{2}

= 2^{2}

使用根式运算法则:

n a^{n} = a

2^{2} = 2

= 2

= \frac{5}{2}

= ln (\frac{1}{2} + \frac{5}{2})

化简

\frac{1}{2} + \frac{5}{2} : \frac{1 + 5}{2}

\frac{1}{2} + \frac{5}{2}

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 + 5}{2}

= ln (\frac{1 + 5}{2})

= ln (\frac{1 + 5}{2})

= ln (\frac{1 + 5}{2})

流行的例子

cot^{7/4}(pi/4)

cot^{\frac{7}{4}} (\frac{π}{4})

12 cos (6 5^{\circ})

tan (3 0^{\circ}) \cdot 8

sin^2(30)cos^2(30)

sin^{2} (3 0^{\circ}) cos^{2} (3 0^{\circ})

sin^{2} (2 9^{\circ})