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受欢迎的三角函数 >

2sin(pi/4-x)+sqrt(3)=0

解答

2 sin (\frac{π}{4} - x) + 3 = 0

解答

x = - 2 πn - \frac{13 π}{12}, x = - 2 πn - \frac{17 π}{12}

+1

度数

x = - 19 5^{\circ} - 36 0^{\circ} n, x = - 25 5^{\circ} - 36 0^{\circ} n

求解步骤

2 sin (\frac{π}{4} - x) + 3 = 0

将

3

到右边

2 sin (\frac{π}{4} - x) + 3 = 0

两边减去

3

2 sin (\frac{π}{4} - x) + 3 - 3 = 0 - 3

化简

2 sin (\frac{π}{4} - x) = - 3

2 sin (\frac{π}{4} - x) = - 3

两边除以

2

2 sin (\frac{π}{4} - x) = - 3

两边除以

2

\frac{2 sin ( \frac{π}{4} - x )}{2} = \frac{- 3}{2}

化简

sin (\frac{π}{4} - x) = - \frac{3}{2}

sin (\frac{π}{4} - x) = - \frac{3}{2}

sin (\frac{π}{4} - x) = - \frac{3}{2}

的通解

sin (x)

周期表（周期为

2 πn

"）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

\frac{π}{4} - x = \frac{4 π}{3} + 2 πn, \frac{π}{4} - x = \frac{5 π}{3} + 2 πn

\frac{π}{4} - x = \frac{4 π}{3} + 2 πn, \frac{π}{4} - x = \frac{5 π}{3} + 2 πn

解

\frac{π}{4} - x = \frac{4 π}{3} + 2 πn : x = - 2 πn - \frac{13 π}{12}

\frac{π}{4} - x = \frac{4 π}{3} + 2 πn

将

\frac{π}{4}

到右边

\frac{π}{4} - x = \frac{4 π}{3} + 2 πn

两边减去

\frac{π}{4}

\frac{π}{4} - x - \frac{π}{4} = \frac{4 π}{3} + 2 πn - \frac{π}{4}

化简

\frac{π}{4} - x - \frac{π}{4} = \frac{4 π}{3} + 2 πn - \frac{π}{4}

化简

\frac{π}{4} - x - \frac{π}{4} : - x

\frac{π}{4} - x - \frac{π}{4}

同类项相加:

\frac{π}{4} - \frac{π}{4} = 0

= - x

化简

\frac{4 π}{3} + 2 πn - \frac{π}{4} : 2 πn + \frac{13 π}{12}

\frac{4 π}{3} + 2 πn - \frac{π}{4}

对同类项分组

= 2 πn - \frac{π}{4} + \frac{4 π}{3}

4, 3

的最小公倍数:

12

4, 3

最小公倍数 (LCM)

4

质因数分解:

2 \cdot 2

4

4

除以

24 = 2 \cdot 2

= 2 \cdot 2

3

质因数分解:

3

3

3

是质数，因此无法因数分解

= 3

将每个因子乘以它在

4

或

3

中出现的最多次数

= 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}{4} :

将分母和分子乘以

3

\frac{π}{4} = \frac{π 3}{4 \cdot 3} = \frac{π 3}{12}

对于

\frac{4 π}{3} :

将分母和分子乘以

4

\frac{4 π}{3} = \frac{4 π 4}{3 \cdot 4} = \frac{16 π}{12}

= - \frac{π 3}{12} + \frac{16 π}{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 3 + 16 π}{12}

同类项相加:

- 3 π + 16 π = 13 π

= 2 πn + \frac{13 π}{12}

- x = 2 πn + \frac{13 π}{12}

- x = 2 πn + \frac{13 π}{12}

- x = 2 πn + \frac{13 π}{12}

两边除以

- 1

- x = 2 πn + \frac{13 π}{12}

两边除以

- 1

\frac{- x}{- 1} = \frac{2 πn}{- 1} + \frac{\frac{13 π}{12}}{- 1}

化简

\frac{- x}{- 1} = \frac{2 πn}{- 1} + \frac{\frac{13 π}{12}}{- 1}

化简

\frac{- x}{- 1} : x

\frac{- x}{- 1}

使用分式法则:

\frac{- a}{- b} = \frac{a}{b}

= \frac{x}{1}

使用法则

\frac{a}{1} = a

= x

化简

\frac{2 πn}{- 1} + \frac{\frac{13 π}{12}}{- 1} : - 2 πn - \frac{13 π}{12}

\frac{2 πn}{- 1} + \frac{\frac{13 π}{12}}{- 1}

\frac{2 πn}{- 1} = - 2 πn

\frac{2 πn}{- 1}

使用分式法则:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{2 πn}{1}

使用法则

\frac{a}{1} = a

= - 2 πn

= - 2 πn + \frac{\frac{13 π}{12}}{- 1}

\frac{\frac{13 π}{12}}{- 1} = - \frac{13 π}{12}

\frac{\frac{13 π}{12}}{- 1}

使用分式法则:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{\frac{13 π}{12}}{1}

使用分式法则:

\frac{a}{1} = a

\frac{\frac{13 π}{12}}{1} = \frac{13 π}{12}

= - \frac{13 π}{12}

= - 2 πn - \frac{13 π}{12}

x = - 2 πn - \frac{13 π}{12}

x = - 2 πn - \frac{13 π}{12}

x = - 2 πn - \frac{13 π}{12}

解

\frac{π}{4} - x = \frac{5 π}{3} + 2 πn : x = - 2 πn - \frac{17 π}{12}

\frac{π}{4} - x = \frac{5 π}{3} + 2 πn

将

\frac{π}{4}

到右边

\frac{π}{4} - x = \frac{5 π}{3} + 2 πn

两边减去

\frac{π}{4}

\frac{π}{4} - x - \frac{π}{4} = \frac{5 π}{3} + 2 πn - \frac{π}{4}

化简

\frac{π}{4} - x - \frac{π}{4} = \frac{5 π}{3} + 2 πn - \frac{π}{4}

化简

\frac{π}{4} - x - \frac{π}{4} : - x

\frac{π}{4} - x - \frac{π}{4}

同类项相加:

\frac{π}{4} - \frac{π}{4} = 0

= - x

化简

\frac{5 π}{3} + 2 πn - \frac{π}{4} : 2 πn + \frac{17 π}{12}

\frac{5 π}{3} + 2 πn - \frac{π}{4}

对同类项分组

= 2 πn - \frac{π}{4} + \frac{5 π}{3}

4, 3

的最小公倍数:

12

4, 3

最小公倍数 (LCM)

4

质因数分解:

2 \cdot 2

4

4

除以

24 = 2 \cdot 2

= 2 \cdot 2

3

质因数分解:

3

3

3

是质数，因此无法因数分解

= 3

将每个因子乘以它在

4

或

3

中出现的最多次数

= 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}{4} :

将分母和分子乘以

3

\frac{π}{4} = \frac{π 3}{4 \cdot 3} = \frac{π 3}{12}

对于

\frac{5 π}{3} :

将分母和分子乘以

4

\frac{5 π}{3} = \frac{5 π 4}{3 \cdot 4} = \frac{20 π}{12}

= - \frac{π 3}{12} + \frac{20 π}{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 3 + 20 π}{12}

同类项相加:

- 3 π + 20 π = 17 π

= 2 πn + \frac{17 π}{12}

- x = 2 πn + \frac{17 π}{12}

- x = 2 πn + \frac{17 π}{12}

- x = 2 πn + \frac{17 π}{12}

两边除以

- 1

- x = 2 πn + \frac{17 π}{12}

两边除以

- 1

\frac{- x}{- 1} = \frac{2 πn}{- 1} + \frac{\frac{17 π}{12}}{- 1}

化简

\frac{- x}{- 1} = \frac{2 πn}{- 1} + \frac{\frac{17 π}{12}}{- 1}

化简

\frac{- x}{- 1} : x

\frac{- x}{- 1}

使用分式法则:

\frac{- a}{- b} = \frac{a}{b}

= \frac{x}{1}

使用法则

\frac{a}{1} = a

= x

化简

\frac{2 πn}{- 1} + \frac{\frac{17 π}{12}}{- 1} : - 2 πn - \frac{17 π}{12}

\frac{2 πn}{- 1} + \frac{\frac{17 π}{12}}{- 1}

\frac{2 πn}{- 1} = - 2 πn

\frac{2 πn}{- 1}

使用分式法则:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{2 πn}{1}

使用法则

\frac{a}{1} = a

= - 2 πn

= - 2 πn + \frac{\frac{17 π}{12}}{- 1}

\frac{\frac{17 π}{12}}{- 1} = - \frac{17 π}{12}

\frac{\frac{17 π}{12}}{- 1}

使用分式法则:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{\frac{17 π}{12}}{1}

使用分式法则:

\frac{a}{1} = a

\frac{\frac{17 π}{12}}{1} = \frac{17 π}{12}

= - \frac{17 π}{12}

= - 2 πn - \frac{17 π}{12}

x = - 2 πn - \frac{17 π}{12}

x = - 2 πn - \frac{17 π}{12}

x = - 2 πn - \frac{17 π}{12}

x = - 2 πn - \frac{13 π}{12}, x = - 2 πn - \frac{17 π}{12}

作图

流行的例子

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