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受欢迎的三角函数 >

sin(2x-23)=-(sqrt(2))/2

解答

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

解答

x = 18 0^{\circ} n + 12 4^{\circ}, x = 18 0^{\circ} n + 16 9^{\circ}

+1

弧度

x = \frac{31 π}{45} + πn, x = \frac{169 π}{180} + πn

求解步骤

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

sin (2 x - 2 3^{\circ}) = - \frac{2}{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 - 2 3^{\circ} = 22 5^{\circ} + 36 0^{\circ} n, 2 x - 2 3^{\circ} = 31 5^{\circ} + 36 0^{\circ} n

2 x - 2 3^{\circ} = 22 5^{\circ} + 36 0^{\circ} n, 2 x - 2 3^{\circ} = 31 5^{\circ} + 36 0^{\circ} n

解

2 x - 2 3^{\circ} = 22 5^{\circ} + 36 0^{\circ} n : x = 18 0^{\circ} n + 12 4^{\circ}

2 x - 2 3^{\circ} = 22 5^{\circ} + 36 0^{\circ} n

将

2 3^{\circ}

到右边

2 x - 2 3^{\circ} = 22 5^{\circ} + 36 0^{\circ} n

两边加上

2 3^{\circ}

2 x - 2 3^{\circ} + 2 3^{\circ} = 22 5^{\circ} + 36 0^{\circ} n + 2 3^{\circ}

化简

2 x - 2 3^{\circ} + 2 3^{\circ} = 22 5^{\circ} + 36 0^{\circ} n + 2 3^{\circ}

化简

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

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

同类项相加:

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

= 2 x

化简

22 5^{\circ} + 36 0^{\circ} n + 2 3^{\circ} : 36 0^{\circ} n + 24 8^{\circ}

22 5^{\circ} + 36 0^{\circ} n + 2 3^{\circ}

对同类项分组

= 36 0^{\circ} n + 22 5^{\circ} + 2 3^{\circ}

4, 180

的最小公倍数:

180

4, 180

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

180

质因数分解:

2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

180

180

除以

2180 = 90 \cdot 2

= 2 \cdot 90

90

除以

290 = 45 \cdot 2

= 2 \cdot 2 \cdot 45

45

除以

345 = 15 \cdot 3

= 2 \cdot 2 \cdot 3 \cdot 15

15

除以

315 = 5 \cdot 3

= 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

2, 3, 5

都是质数，因此无法进一步因数分解

= 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

将每个因子乘以它在

4

或

180

中出现的最多次数

= 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

数字相乘:

2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 = 180

= 180

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

180

对于

22 5^{\circ} :

将分母和分子乘以

45

22 5^{\circ} = \frac{90 0 ^{\circ} 45}{4 \cdot 45} = 22 5^{\circ}

= 22 5^{\circ} + 2 3^{\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{4050 0 ^{\circ} + 414 0 ^{\circ}}{180}

同类项相加:

4050 0^{\circ} + 414 0^{\circ} = 4464 0^{\circ}

= 24 8^{\circ}

约分:

4

= 36 0^{\circ} n + 24 8^{\circ}

2 x = 36 0^{\circ} n + 24 8^{\circ}

2 x = 36 0^{\circ} n + 24 8^{\circ}

2 x = 36 0^{\circ} n + 24 8^{\circ}

两边除以

2

2 x = 36 0^{\circ} n + 24 8^{\circ}

两边除以

2

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{24 8 ^{\circ}}{2}

化简

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{24 8 ^{\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{24 8 ^{\circ}}{2} : 18 0^{\circ} n + 12 4^{\circ}

\frac{36 0 ^{\circ} n}{2} + \frac{24 8 ^{\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{24 8 ^{\circ}}{2} = 12 4^{\circ}

\frac{24 8 ^{\circ}}{2}

使用分式法则:

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

= \frac{1116 0 ^{\circ}}{45 \cdot 2}

数字相乘:

45 \cdot 2 = 90

= 12 4^{\circ}

约分:

2

= 12 4^{\circ}

= 18 0^{\circ} n + 12 4^{\circ}

x = 18 0^{\circ} n + 12 4^{\circ}

x = 18 0^{\circ} n + 12 4^{\circ}

x = 18 0^{\circ} n + 12 4^{\circ}

解

2 x - 2 3^{\circ} = 31 5^{\circ} + 36 0^{\circ} n : x = 18 0^{\circ} n + 16 9^{\circ}

2 x - 2 3^{\circ} = 31 5^{\circ} + 36 0^{\circ} n

将

2 3^{\circ}

到右边

2 x - 2 3^{\circ} = 31 5^{\circ} + 36 0^{\circ} n

两边加上

2 3^{\circ}

2 x - 2 3^{\circ} + 2 3^{\circ} = 31 5^{\circ} + 36 0^{\circ} n + 2 3^{\circ}

化简

2 x - 2 3^{\circ} + 2 3^{\circ} = 31 5^{\circ} + 36 0^{\circ} n + 2 3^{\circ}

化简

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

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

同类项相加:

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

= 2 x

化简

31 5^{\circ} + 36 0^{\circ} n + 2 3^{\circ} : 36 0^{\circ} n + 33 8^{\circ}

31 5^{\circ} + 36 0^{\circ} n + 2 3^{\circ}

对同类项分组

= 36 0^{\circ} n + 31 5^{\circ} + 2 3^{\circ}

4, 180

的最小公倍数:

180

4, 180

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

180

质因数分解:

2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

180

180

除以

2180 = 90 \cdot 2

= 2 \cdot 90

90

除以

290 = 45 \cdot 2

= 2 \cdot 2 \cdot 45

45

除以

345 = 15 \cdot 3

= 2 \cdot 2 \cdot 3 \cdot 15

15

除以

315 = 5 \cdot 3

= 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

2, 3, 5

都是质数，因此无法进一步因数分解

= 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

将每个因子乘以它在

4

或

180

中出现的最多次数

= 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

数字相乘:

2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 = 180

= 180

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

180

对于

31 5^{\circ} :

将分母和分子乘以

45

31 5^{\circ} = \frac{126 0 ^{\circ} 45}{4 \cdot 45} = 31 5^{\circ}

= 31 5^{\circ} + 2 3^{\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{5670 0 ^{\circ} + 414 0 ^{\circ}}{180}

同类项相加:

5670 0^{\circ} + 414 0^{\circ} = 6084 0^{\circ}

= 33 8^{\circ}

约分:

2

= 36 0^{\circ} n + 33 8^{\circ}

2 x = 36 0^{\circ} n + 33 8^{\circ}

2 x = 36 0^{\circ} n + 33 8^{\circ}

2 x = 36 0^{\circ} n + 33 8^{\circ}

两边除以

2

2 x = 36 0^{\circ} n + 33 8^{\circ}

两边除以

2

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{33 8 ^{\circ}}{2}

化简

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{33 8 ^{\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{33 8 ^{\circ}}{2} : 18 0^{\circ} n + 16 9^{\circ}

\frac{36 0 ^{\circ} n}{2} + \frac{33 8 ^{\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{33 8 ^{\circ}}{2} = 16 9^{\circ}

\frac{33 8 ^{\circ}}{2}

使用分式法则:

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

= \frac{3042 0 ^{\circ}}{90 \cdot 2}

数字相乘:

90 \cdot 2 = 180

= 16 9^{\circ}

= 18 0^{\circ} n + 16 9^{\circ}

x = 18 0^{\circ} n + 16 9^{\circ}

x = 18 0^{\circ} n + 16 9^{\circ}

x = 18 0^{\circ} n + 16 9^{\circ}

x = 18 0^{\circ} n + 12 4^{\circ}, x = 18 0^{\circ} n + 16 9^{\circ}

作图

流行的例子

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sin(x)cos(x)cos(2x)= 1/8

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