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受欢迎的三角函数 >

arccos((13)/(sqrt(6*\sqrt{86))})

解答

arccos (\frac{13}{6 \cdot 86})

解答

x \in R 无解

求解步骤

arccos (\frac{13}{6 86})

化简:

\frac{13}{6 86} = \frac{13 3 4 2 \cdot 4 3 ^{\frac{3}{4}}}{258}

\frac{13}{6 86}

686 = 3 \cdot 2^{\frac{3}{4}} 443

686

使用根式运算法则:

n ab = n a n b,

假定

a \geq 0, b \geq 0

= 686

86 : 486

使用根式运算法则:

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

= (8 6^{\frac{1}{2}})^{\frac{1}{2}}

使用指数法则:

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

= 8 6^{\frac{1}{2} \cdot \frac{1}{2}}

\frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}

\frac{1}{2} \cdot \frac{1}{2}

分式相乘:

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

= \frac{1 \cdot 1}{2 \cdot 2}

数字相乘:

1 \cdot 1 = 1

= \frac{1}{2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

= \frac{1}{4}

= 8 6^{\frac{1}{4}}

a^{\frac{1}{n}} = n a

= 486

= 6486

分解整数

6 = 2 \cdot 3

= 2 \cdot 3 486

使用根式运算法则:

n ab = n a n b

2 \cdot 3 = 23

= 23486

分解整数

86 = 2 \cdot 43

= 23 4 2 \cdot 43

使用根式运算法则:

n ab = n a n b

4 2 \cdot 43 = 42443

= 2342443

使用指数法则:

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

242 = 2^{\frac{1}{2}} \cdot 2^{\frac{1}{4}} = 2^{\frac{1}{2} + \frac{1}{4}}

= 3 \cdot 2^{\frac{1}{2} + \frac{1}{4}} 443

2^{\frac{1}{2} + \frac{1}{4}} = 2^{\frac{3}{4}}

2^{\frac{1}{2} + \frac{1}{4}}

化简

\frac{1}{2} + \frac{1}{4} : \frac{3}{4}

\frac{1}{2} + \frac{1}{4}

2, 4

的最小公倍数:

4

2, 4

最小公倍数 (LCM)

2

质因数分解:

2

2

2

是质数，因此无法因数分解

= 2

4

质因数分解:

2 \cdot 2

4

4

除以

24 = 2 \cdot 2

= 2 \cdot 2

将每个因子乘以它在

2

或

4

中出现的最多次数

= 2 \cdot 2

数字相乘:

2 \cdot 2 = 4

= 4

根据最小公倍数调整分式

将每个分子乘以其分母转变为最小公倍数所要乘以的同一数值

4

对于

\frac{1}{2} :

将分母和分子乘以

2

\frac{1}{2} = \frac{1 \cdot 2}{2 \cdot 2} = \frac{2}{4}

= \frac{2}{4} + \frac{1}{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{2 + 1}{4}

数字相加:

2 + 1 = 3

= \frac{3}{4}

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

= 3 \cdot 2^{\frac{3}{4}} 443

= \frac{13}{3 \cdot 2 ^{\frac{3}{4}} 4 43}

\frac{13}{3 \cdot 2 ^{\frac{3}{4}} 4 43}

有理化:

\frac{13 3 4 2 \cdot 4 3 ^{\frac{3}{4}}}{258}

\frac{13}{3 \cdot 2 ^{\frac{3}{4}} 4 43}

乘以共轭根式

\frac{3}{3}

= \frac{13 3}{3 \cdot 2 ^{\frac{3}{4}} 4 43 3}

3 \cdot 2^{\frac{3}{4}} 4433 = 3 \cdot 2^{\frac{3}{4}} 443

3 \cdot 2^{\frac{3}{4}} 4433

使用根式运算法则:

a a = a

33 = 3

= 3 \cdot 2^{\frac{3}{4}} 443

= \frac{13 3}{3 \cdot 2 ^{\frac{3}{4}} 4 43}

乘以共轭根式

\frac{4 2}{4 2}

= \frac{13 3 4 2}{3 \cdot 2 ^{\frac{3}{4}} 4 43 4 2}

3 \cdot 2^{\frac{3}{4}} 44342 = 6443

3 \cdot 2^{\frac{3}{4}} 44342

使用指数法则:

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

2^{\frac{3}{4}} 42 = 2^{\frac{3}{4}} \cdot 2^{\frac{1}{4}} = 2^{\frac{3}{4} + \frac{1}{4}}

= 3443 \cdot 2^{\frac{3}{4} + \frac{1}{4}}

2^{\frac{3}{4} + \frac{1}{4}} = 2

2^{\frac{3}{4} + \frac{1}{4}}

合并分式

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

使用法则

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

= \frac{3 + 1}{4}

数字相加:

3 + 1 = 4

= \frac{4}{4}

使用法则

\frac{a}{a} = 1

= 1

= 2^{1}

使用法则

a^{1} = a

= 2

= 3 \cdot 2443

数字相乘:

3 \cdot 2 = 6

= 6443

= \frac{13 3 4 2}{6 4 43}

乘以共轭根式

\frac{4 3 ^{\frac{3}{4}}}{4 3 ^{\frac{3}{4}}}

= \frac{13 3 4 2 \cdot 4 3 ^{\frac{3}{4}}}{6 4 43 \cdot 4 3 ^{\frac{3}{4}}}

6443 \cdot 4 3^{\frac{3}{4}} = 258

6443 \cdot 4 3^{\frac{3}{4}}

使用指数法则:

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

4 3^{\frac{3}{4}} 443 = 4 3^{\frac{3}{4}} \cdot 4 3^{\frac{1}{4}} = 4 3^{\frac{3}{4} + \frac{1}{4}}

= 6 \cdot 4 3^{\frac{3}{4} + \frac{1}{4}}

4 3^{\frac{3}{4} + \frac{1}{4}} = 43

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

合并分式

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

使用法则

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

= \frac{3 + 1}{4}

数字相加:

3 + 1 = 4

= \frac{4}{4}

使用法则

\frac{a}{a} = 1

= 1

= 4 3^{1}

使用法则

a^{1} = a

= 43

= 6 \cdot 43

数字相乘:

6 \cdot 43 = 258

= 258

= \frac{13 3 4 2 \cdot 4 3 ^{\frac{3}{4}}}{258}

= \frac{13 3 4 2 \cdot 4 3 ^{\frac{3}{4}}}{258}

= arccos (\frac{13 3 4 2 \cdot 4 3 ^{\frac{3}{4}}}{258})

arccos (x)

的实数域为

- 1 \leq x \leq 1

x \in R 无解

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\frac{cos ^{2} ( \frac{π}{4} )}{2}

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29 \cdot cos (- 5.9 1^{\circ})

2(1)^2+2arcsin(1)

2 (1)^{2} + 2 arcsin (1)