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受欢迎的三角函数 >

arccosh(5/4)

解答

arccosh (\frac{5}{4})

解答

ln (2)

+1

十进制

0.69314 \dots

求解步骤

arccosh (\frac{5}{4})

使用双曲函数恒等式:

arccosh (x) = ln (x + x^{2} - 1)

= ln \frac{5}{4} + (\frac{5}{4})^{2} - 1

ln \frac{5}{4} + (\frac{5}{4})^{2} - 1 = ln (2)

ln \frac{5}{4} + (\frac{5}{4})^{2} - 1

(\frac{5}{4})^{2} - 1 = \frac{3}{4}

(\frac{5}{4})^{2} - 1

(\frac{5}{4})^{2} = \frac{25}{16}

(\frac{5}{4})^{2}

使用指数法则:

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

= \frac{5 ^{2}}{4 ^{2}}

5^{2} = 25

= \frac{25}{4 ^{2}}

4^{2} = 16

= \frac{25}{16}

= \frac{25}{16} - 1

化简

\frac{25}{16} - 1 : \frac{9}{16}

\frac{25}{16} - 1

将项转换为分式:

1 = \frac{1 \cdot 16}{16}

= \frac{25}{16} - \frac{1 \cdot 16}{16}

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{25 - 1 \cdot 16}{16}

25 - 1 \cdot 16 = 9

25 - 1 \cdot 16

数字相乘:

1 \cdot 16 = 16

= 25 - 16

数字相减:

25 - 16 = 9

= 9

= \frac{9}{16}

= \frac{9}{16}

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{9}{16}

16 = 4

16

因式分解数字:

16 = 4^{2}

= 4^{2}

使用根式运算法则:

n a^{n} = a

4^{2} = 4

= 4

= \frac{9}{4}

9 = 3

9

因式分解数字:

9 = 3^{2}

= 3^{2}

使用根式运算法则:

n a^{n} = a

3^{2} = 3

= 3

= \frac{3}{4}

= ln (\frac{5}{4} + \frac{3}{4})

化简

\frac{5}{4} + \frac{3}{4} : 2

\frac{5}{4} + \frac{3}{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{5 + 3}{4}

数字相加:

5 + 3 = 8

= \frac{8}{4}

数字相除:

\frac{8}{4} = 2

= 2

= ln (2)

= ln (2)

流行的例子

- 8.4 \cdot cos (11 0^{\circ})

1 \cdot sin (4 5^{\circ})

(cos^4(pi/4))/4

\frac{cos ^{4} ( \frac{π}{4} )}{4}

sin (0.51)

sin (0.57)