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受欢迎的三角函数 >

12.4-10(0.5pi-arcsin(0.5)-0.5(1-(0.5)^2)^{1/2})

解答

12.4 - 10 (0.5 π - arcsin (0.5) - 0.5 (1 - (0.5)^{2})^{\frac{1}{2}})

解答

\frac{62}{5} - \frac{5 ( 4 π - 3 \cdot 3 ^{\frac{1}{2}} )}{6}

+1

十进制

358.57

求解步骤

12.4 - 10 (0.5 π - arcsin (0.5) - 0.5 (1 - (0.5)^{2})^{\frac{1}{2}})

= \frac{62}{5} - 10 \frac{1}{2} π - arcsin (\frac{1}{2}) - \frac{1}{2} (1 - (\frac{1}{2})^{2})^{\frac{1}{2}}

使用以下普通恒等式:

arcsin (\frac{1}{2}) = \frac{π}{6}

arcsin (\frac{1}{2})

x 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arcsin (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arcsin (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= \frac{π}{6}

= \frac{62}{5} - 10 \frac{1}{2} π - \frac{π}{6} - \frac{1}{2} (1 - (\frac{1}{2})^{2})^{\frac{1}{2}}

化简

\frac{62}{5} - 10 \frac{1}{2} π - \frac{π}{6} - \frac{1}{2} (1 - (\frac{1}{2})^{2})^{\frac{1}{2}} : \frac{62}{5} - \frac{5 ( 4 π - 3 \cdot 3 ^{\frac{1}{2}} )}{6}

\frac{62}{5} - 10 \frac{1}{2} π - \frac{π}{6} - \frac{1}{2} (1 - (\frac{1}{2})^{2})^{\frac{1}{2}}

10 \frac{1}{2} π - \frac{π}{6} - \frac{1}{2} (1 - (\frac{1}{2})^{2})^{\frac{1}{2}} = \frac{5 ( 4 π - 3 \cdot 3 ^{\frac{1}{2}} )}{6}

10 \frac{1}{2} π - \frac{π}{6} - \frac{1}{2} (1 - (\frac{1}{2})^{2})^{\frac{1}{2}}

\frac{1}{2} π = \frac{π}{2}

\frac{1}{2} π

分式相乘:

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

= \frac{1 π}{2}

乘以:

1 π = π

= \frac{π}{2}

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

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

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

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

(\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}

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

化简

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

1 - \frac{1}{4}

将项转换为分式:

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

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

1 \cdot 4 - 1 = 3

1 \cdot 4 - 1

数字相乘:

1 \cdot 4 = 4

= 4 - 1

数字相减:

4 - 1 = 3

= 3

= \frac{3}{4}

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

使用根式运算法则:

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

假定

a \geq 0, b \geq 0

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

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

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

因式分解数字:

4 = 2^{2}

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

使用指数法则:

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

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

= 2

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

= \frac{1}{2} \cdot \frac{3 ^{\frac{1}{2}}}{2}

分式相乘:

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

= \frac{1 \cdot 3 ^{\frac{1}{2}}}{2 \cdot 2}

乘以:

1 \cdot 3^{\frac{1}{2}} = 3^{\frac{1}{2}}

= \frac{3 ^{\frac{1}{2}}}{2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

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

= 10 (\frac{π}{2} - \frac{π}{6} - \frac{3 ^{\frac{1}{2}}}{4})

化简

\frac{π}{2} - \frac{π}{6} - \frac{3 ^{\frac{1}{2}}}{4} : \frac{4 π - 3 \cdot 3 ^{\frac{1}{2}}}{12}

\frac{π}{2} - \frac{π}{6} - \frac{3 ^{\frac{1}{2}}}{4}

2, 6, 4

的最小公倍数:

12

2, 6, 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

6

质因数分解:

2 \cdot 3

6

6

除以

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

都是质数，因此无法进一步因数分解

= 2 \cdot 3

4

质因数分解:

2 \cdot 2

4

4

除以

24 = 2 \cdot 2

= 2 \cdot 2

计算出由至少在以下一个数字中出现的因数组成的数字:

2, 6, 4

= 2 \cdot 2 \cdot 3

数字相乘:

2 \cdot 2 \cdot 3 = 12

= 12

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

12

对于

\frac{π}{2} :

将分母和分子乘以

6

\frac{π}{2} = \frac{π 6}{2 \cdot 6} = \frac{π 6}{12}

对于

\frac{π}{6} :

将分母和分子乘以

2

\frac{π}{6} = \frac{π 2}{6 \cdot 2} = \frac{π 2}{12}

对于

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

将分母和分子乘以

3

\frac{3 ^{\frac{1}{2}}}{4} = \frac{3 ^{\frac{1}{2}} \cdot 3}{4 \cdot 3} = \frac{3 ^{\frac{1}{2}} \cdot 3}{12}

= \frac{π 6}{12} - \frac{π 2}{12} - \frac{3 ^{\frac{1}{2}} \cdot 3}{12}

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{π 6 - π 2 - 3 ^{\frac{1}{2}} \cdot 3}{12}

同类项相加:

6 π - 2 π = 4 π

= \frac{4 π - 3 \cdot 3 ^{\frac{1}{2}}}{12}

= 10 \cdot \frac{4 π - 3 \cdot 3 ^{\frac{1}{2}}}{12}

分式相乘:

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

= \frac{( 4 π - 3 ^{\frac{1}{2}} \cdot 3 ) \cdot 10}{12}

约分:

2

= \frac{5 ( 4 π - 3 \cdot 3 ^{\frac{1}{2}} )}{6}

= \frac{62}{5} - \frac{5 ( 4 π - 3 \cdot 3 ^{\frac{1}{2}} )}{6}

= \frac{62}{5} - \frac{5 ( 4 π - 3 \cdot 3 ^{\frac{1}{2}} )}{6}

流行的例子

sin (\frac{11}{9}) π

(1.24)/(tan(34))

\frac{1.24}{tan ( 3 4 ^{\circ} )}

(sin(30))/(sin(22))

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

tan (21. 8^{\circ}) 2

12.1 cos (3 0^{\circ})