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受欢迎的三角函数 >

sin(2x+30)=-(sqrt(3))/2

解答

sin (2 x + 3 0^{\circ}) = - \frac{3}{2}

解答

x = 18 0^{\circ} n + 10 5^{\circ}, x = 18 0^{\circ} n + 13 5^{\circ}

+1

弧度

x = \frac{7 π}{12} + πn, x = \frac{3 π}{4} + πn

求解步骤

sin (2 x + 3 0^{\circ}) = - \frac{3}{2}

sin (2 x + 3 0^{\circ}) = - \frac{3}{2}

的通解

sin (x)

周期表（周期为

36 0^{\circ} n

"）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

2 x + 3 0^{\circ} = 24 0^{\circ} + 36 0^{\circ} n, 2 x + 3 0^{\circ} = 30 0^{\circ} + 36 0^{\circ} n

2 x + 3 0^{\circ} = 24 0^{\circ} + 36 0^{\circ} n, 2 x + 3 0^{\circ} = 30 0^{\circ} + 36 0^{\circ} n

解

2 x + 3 0^{\circ} = 24 0^{\circ} + 36 0^{\circ} n : x = 18 0^{\circ} n + 10 5^{\circ}

2 x + 3 0^{\circ} = 24 0^{\circ} + 36 0^{\circ} n

将

3 0^{\circ}

到右边

2 x + 3 0^{\circ} = 24 0^{\circ} + 36 0^{\circ} n

两边减去

3 0^{\circ}

2 x + 3 0^{\circ} - 3 0^{\circ} = 24 0^{\circ} + 36 0^{\circ} n - 3 0^{\circ}

化简

2 x + 3 0^{\circ} - 3 0^{\circ} = 24 0^{\circ} + 36 0^{\circ} n - 3 0^{\circ}

化简

2 x + 3 0^{\circ} - 3 0^{\circ} : 2 x

2 x + 3 0^{\circ} - 3 0^{\circ}

同类项相加:

3 0^{\circ} - 3 0^{\circ} = 0

= 2 x

化简

24 0^{\circ} + 36 0^{\circ} n - 3 0^{\circ} : 36 0^{\circ} n + 21 0^{\circ}

24 0^{\circ} + 36 0^{\circ} n - 3 0^{\circ}

对同类项分组

= 36 0^{\circ} n - 3 0^{\circ} + 24 0^{\circ}

6, 3

的最小公倍数:

6

6, 3

最小公倍数 (LCM)

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

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

6

或

3

中出现的最多次数

= 2 \cdot 3

数字相乘:

2 \cdot 3 = 6

= 6

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

6

对于

24 0^{\circ} :

将分母和分子乘以

2

24 0^{\circ} = \frac{72 0 ^{\circ} 2}{3 \cdot 2} = 24 0^{\circ}

= - 3 0^{\circ} + 24 0^{\circ}

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{- 18 0 ^{\circ} + 144 0 ^{\circ}}{6}

同类项相加:

- 18 0^{\circ} + 144 0^{\circ} = 126 0^{\circ}

= 36 0^{\circ} n + 21 0^{\circ}

2 x = 36 0^{\circ} n + 21 0^{\circ}

2 x = 36 0^{\circ} n + 21 0^{\circ}

2 x = 36 0^{\circ} n + 21 0^{\circ}

两边除以

2

2 x = 36 0^{\circ} n + 21 0^{\circ}

两边除以

2

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{21 0 ^{\circ}}{2}

化简

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{21 0 ^{\circ}}{2}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

\frac{36 0 ^{\circ} n}{2} + \frac{21 0 ^{\circ}}{2} : 18 0^{\circ} n + 10 5^{\circ}

\frac{36 0 ^{\circ} n}{2} + \frac{21 0 ^{\circ}}{2}

\frac{36 0 ^{\circ} n}{2} = 18 0^{\circ} n

\frac{36 0 ^{\circ} n}{2}

数字相除:

\frac{2}{2} = 1

= 18 0^{\circ} n

\frac{21 0 ^{\circ}}{2} = 10 5^{\circ}

\frac{21 0 ^{\circ}}{2}

使用分式法则:

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

= \frac{126 0 ^{\circ}}{6 \cdot 2}

数字相乘:

6 \cdot 2 = 12

= 10 5^{\circ}

= 18 0^{\circ} n + 10 5^{\circ}

x = 18 0^{\circ} n + 10 5^{\circ}

x = 18 0^{\circ} n + 10 5^{\circ}

x = 18 0^{\circ} n + 10 5^{\circ}

解

2 x + 3 0^{\circ} = 30 0^{\circ} + 36 0^{\circ} n : x = 18 0^{\circ} n + 13 5^{\circ}

2 x + 3 0^{\circ} = 30 0^{\circ} + 36 0^{\circ} n

将

3 0^{\circ}

到右边

2 x + 3 0^{\circ} = 30 0^{\circ} + 36 0^{\circ} n

两边减去

3 0^{\circ}

2 x + 3 0^{\circ} - 3 0^{\circ} = 30 0^{\circ} + 36 0^{\circ} n - 3 0^{\circ}

化简

2 x + 3 0^{\circ} - 3 0^{\circ} = 30 0^{\circ} + 36 0^{\circ} n - 3 0^{\circ}

化简

2 x + 3 0^{\circ} - 3 0^{\circ} : 2 x

2 x + 3 0^{\circ} - 3 0^{\circ}

同类项相加:

3 0^{\circ} - 3 0^{\circ} = 0

= 2 x

化简

30 0^{\circ} + 36 0^{\circ} n - 3 0^{\circ} : 36 0^{\circ} n + 27 0^{\circ}

30 0^{\circ} + 36 0^{\circ} n - 3 0^{\circ}

对同类项分组

= 36 0^{\circ} n - 3 0^{\circ} + 30 0^{\circ}

6, 3

的最小公倍数:

6

6, 3

最小公倍数 (LCM)

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

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

6

或

3

中出现的最多次数

= 2 \cdot 3

数字相乘:

2 \cdot 3 = 6

= 6

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

6

对于

30 0^{\circ} :

将分母和分子乘以

2

30 0^{\circ} = \frac{90 0 ^{\circ} 2}{3 \cdot 2} = 30 0^{\circ}

= - 3 0^{\circ} + 30 0^{\circ}

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{- 18 0 ^{\circ} + 180 0 ^{\circ}}{6}

同类项相加:

- 18 0^{\circ} + 180 0^{\circ} = 162 0^{\circ}

= 27 0^{\circ}

约分:

3

= 36 0^{\circ} n + 27 0^{\circ}

2 x = 36 0^{\circ} n + 27 0^{\circ}

2 x = 36 0^{\circ} n + 27 0^{\circ}

2 x = 36 0^{\circ} n + 27 0^{\circ}

两边除以

2

2 x = 36 0^{\circ} n + 27 0^{\circ}

两边除以

2

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{27 0 ^{\circ}}{2}

化简

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{27 0 ^{\circ}}{2}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

\frac{36 0 ^{\circ} n}{2} + \frac{27 0 ^{\circ}}{2} : 18 0^{\circ} n + 13 5^{\circ}

\frac{36 0 ^{\circ} n}{2} + \frac{27 0 ^{\circ}}{2}

\frac{36 0 ^{\circ} n}{2} = 18 0^{\circ} n

\frac{36 0 ^{\circ} n}{2}

数字相除:

\frac{2}{2} = 1

= 18 0^{\circ} n

\frac{27 0 ^{\circ}}{2} = 13 5^{\circ}

\frac{27 0 ^{\circ}}{2}

使用分式法则:

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

= \frac{54 0 ^{\circ}}{2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

= 13 5^{\circ}

= 18 0^{\circ} n + 13 5^{\circ}

x = 18 0^{\circ} n + 13 5^{\circ}

x = 18 0^{\circ} n + 13 5^{\circ}

x = 18 0^{\circ} n + 13 5^{\circ}

x = 18 0^{\circ} n + 10 5^{\circ}, x = 18 0^{\circ} n + 13 5^{\circ}

作图

流行的例子

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