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受欢迎的三角函数 >

sin(2x-50)=-1/2

解答

sin (2 x - 5 0^{\circ}) = - \frac{1}{2}

解答

x = 18 0^{\circ} n + 13 0^{\circ}, x = 18 0^{\circ} n + 19 0^{\circ}

+1

弧度

x = \frac{13 π}{18} + πn, x = \frac{19 π}{18} + πn

求解步骤

sin (2 x - 5 0^{\circ}) = - \frac{1}{2}

sin (2 x - 5 0^{\circ}) = - \frac{1}{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 - 5 0^{\circ} = 21 0^{\circ} + 36 0^{\circ} n, 2 x - 5 0^{\circ} = 33 0^{\circ} + 36 0^{\circ} n

2 x - 5 0^{\circ} = 21 0^{\circ} + 36 0^{\circ} n, 2 x - 5 0^{\circ} = 33 0^{\circ} + 36 0^{\circ} n

解

2 x - 5 0^{\circ} = 21 0^{\circ} + 36 0^{\circ} n : x = 18 0^{\circ} n + 13 0^{\circ}

2 x - 5 0^{\circ} = 21 0^{\circ} + 36 0^{\circ} n

将

5 0^{\circ}

到右边

2 x - 5 0^{\circ} = 21 0^{\circ} + 36 0^{\circ} n

两边加上

5 0^{\circ}

2 x - 5 0^{\circ} + 5 0^{\circ} = 21 0^{\circ} + 36 0^{\circ} n + 5 0^{\circ}

化简

2 x - 5 0^{\circ} + 5 0^{\circ} = 21 0^{\circ} + 36 0^{\circ} n + 5 0^{\circ}

化简

2 x - 5 0^{\circ} + 5 0^{\circ} : 2 x

2 x - 5 0^{\circ} + 5 0^{\circ}

同类项相加:

- 5 0^{\circ} + 5 0^{\circ} = 0

= 2 x

化简

21 0^{\circ} + 36 0^{\circ} n + 5 0^{\circ} : 36 0^{\circ} n + 26 0^{\circ}

21 0^{\circ} + 36 0^{\circ} n + 5 0^{\circ}

对同类项分组

= 36 0^{\circ} n + 21 0^{\circ} + 5 0^{\circ}

6, 18

的最小公倍数:

18

6, 18

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

18

质因数分解:

2 \cdot 3 \cdot 3

18

18

除以

218 = 9 \cdot 2

= 2 \cdot 9

9

除以

39 = 3 \cdot 3

= 2 \cdot 3 \cdot 3

2, 3

都是质数，因此无法进一步因数分解

= 2 \cdot 3 \cdot 3

将每个因子乘以它在

6

或

18

中出现的最多次数

= 2 \cdot 3 \cdot 3

数字相乘:

2 \cdot 3 \cdot 3 = 18

= 18

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

18

对于

21 0^{\circ} :

将分母和分子乘以

3

21 0^{\circ} = \frac{126 0 ^{\circ} 3}{6 \cdot 3} = 21 0^{\circ}

= 21 0^{\circ} + 5 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{378 0 ^{\circ} + 90 0 ^{\circ}}{18}

同类项相加:

378 0^{\circ} + 90 0^{\circ} = 468 0^{\circ}

= 26 0^{\circ}

约分:

2

= 36 0^{\circ} n + 26 0^{\circ}

2 x = 36 0^{\circ} n + 26 0^{\circ}

2 x = 36 0^{\circ} n + 26 0^{\circ}

2 x = 36 0^{\circ} n + 26 0^{\circ}

两边除以

2

2 x = 36 0^{\circ} n + 26 0^{\circ}

两边除以

2

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{26 0 ^{\circ}}{2}

化简

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{26 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{26 0 ^{\circ}}{2} : 18 0^{\circ} n + 13 0^{\circ}

\frac{36 0 ^{\circ} n}{2} + \frac{26 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{26 0 ^{\circ}}{2} = 13 0^{\circ}

\frac{26 0 ^{\circ}}{2}

使用分式法则:

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

= \frac{234 0 ^{\circ}}{9 \cdot 2}

数字相乘:

9 \cdot 2 = 18

= 13 0^{\circ}

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

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

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

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

解

2 x - 5 0^{\circ} = 33 0^{\circ} + 36 0^{\circ} n : x = 18 0^{\circ} n + 19 0^{\circ}

2 x - 5 0^{\circ} = 33 0^{\circ} + 36 0^{\circ} n

将

5 0^{\circ}

到右边

2 x - 5 0^{\circ} = 33 0^{\circ} + 36 0^{\circ} n

两边加上

5 0^{\circ}

2 x - 5 0^{\circ} + 5 0^{\circ} = 33 0^{\circ} + 36 0^{\circ} n + 5 0^{\circ}

化简

2 x - 5 0^{\circ} + 5 0^{\circ} = 33 0^{\circ} + 36 0^{\circ} n + 5 0^{\circ}

化简

2 x - 5 0^{\circ} + 5 0^{\circ} : 2 x

2 x - 5 0^{\circ} + 5 0^{\circ}

同类项相加:

- 5 0^{\circ} + 5 0^{\circ} = 0

= 2 x

化简

33 0^{\circ} + 36 0^{\circ} n + 5 0^{\circ} : 36 0^{\circ} n + 38 0^{\circ}

33 0^{\circ} + 36 0^{\circ} n + 5 0^{\circ}

对同类项分组

= 36 0^{\circ} n + 33 0^{\circ} + 5 0^{\circ}

6, 18

的最小公倍数:

18

6, 18

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

18

质因数分解:

2 \cdot 3 \cdot 3

18

18

除以

218 = 9 \cdot 2

= 2 \cdot 9

9

除以

39 = 3 \cdot 3

= 2 \cdot 3 \cdot 3

2, 3

都是质数，因此无法进一步因数分解

= 2 \cdot 3 \cdot 3

将每个因子乘以它在

6

或

18

中出现的最多次数

= 2 \cdot 3 \cdot 3

数字相乘:

2 \cdot 3 \cdot 3 = 18

= 18

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

18

对于

33 0^{\circ} :

将分母和分子乘以

3

33 0^{\circ} = \frac{198 0 ^{\circ} 3}{6 \cdot 3} = 33 0^{\circ}

= 33 0^{\circ} + 5 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{594 0 ^{\circ} + 90 0 ^{\circ}}{18}

同类项相加:

594 0^{\circ} + 90 0^{\circ} = 684 0^{\circ}

= 38 0^{\circ}

约分:

2

= 36 0^{\circ} n + 38 0^{\circ}

2 x = 36 0^{\circ} n + 38 0^{\circ}

2 x = 36 0^{\circ} n + 38 0^{\circ}

2 x = 36 0^{\circ} n + 38 0^{\circ}

两边除以

2

2 x = 36 0^{\circ} n + 38 0^{\circ}

两边除以

2

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{38 0 ^{\circ}}{2}

化简

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2} + \frac{38 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{38 0 ^{\circ}}{2} : 18 0^{\circ} n + 19 0^{\circ}

\frac{36 0 ^{\circ} n}{2} + \frac{38 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{38 0 ^{\circ}}{2} = 19 0^{\circ}

\frac{38 0 ^{\circ}}{2}

使用分式法则:

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

= \frac{342 0 ^{\circ}}{9 \cdot 2}

数字相乘:

9 \cdot 2 = 18

= 19 0^{\circ}

= 18 0^{\circ} n + 19 0^{\circ}

x = 18 0^{\circ} n + 19 0^{\circ}

x = 18 0^{\circ} n + 19 0^{\circ}

x = 18 0^{\circ} n + 19 0^{\circ}

x = 18 0^{\circ} n + 13 0^{\circ}, x = 18 0^{\circ} n + 19 0^{\circ}

作图

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