zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

2sin(4x)-1=0,-2pi<= x<= 3pi

解答

2 sin (4 x) - 1 = 0, - 2 π \leq x \leq 3 π

解答

x = \frac{π}{24}, x = \frac{5 π}{24}, x = \frac{13 π}{24}, x = \frac{17 π}{24}, x = \frac{25 π}{24}, x = \frac{29 π}{24}, x = \frac{37 π}{24}, x = \frac{41 π}{24}, x = \frac{49 π}{24}, x = \frac{53 π}{24}, x = - \frac{11 π}{24}, x = - \frac{7 π}{24}, x = - \frac{23 π}{24}, x = - \frac{19 π}{24}, x = - \frac{35 π}{24}, x = - \frac{31 π}{24}, x = - \frac{47 π}{24}, x = - \frac{43 π}{24}

+1

度数

x = 7. 5^{\circ}, x = 37. 5^{\circ}, x = 97. 5^{\circ}, x = 127. 5^{\circ}, x = 187. 5^{\circ}, x = 217. 5^{\circ}, x = 277. 5^{\circ}, x = 307. 5^{\circ}, x = 367. 5^{\circ}, x = 397. 5^{\circ}, x = - 82. 5^{\circ}, x = - 52. 5^{\circ}, x = - 172. 5^{\circ}, x = - 142. 5^{\circ}, x = - 262. 5^{\circ}, x = - 232. 5^{\circ}, x = - 352. 5^{\circ}, x = - 322. 5^{\circ}

求解步骤

2 sin (4 x) - 1 = 0, - 2 π \leq x \leq 3 π

将

1

到右边

2 sin (4 x) - 1 = 0

两边加上

1

2 sin (4 x) - 1 + 1 = 0 + 1

化简

2 sin (4 x) = 1

2 sin (4 x) = 1

两边除以

2

2 sin (4 x) = 1

两边除以

2

\frac{2 sin ( 4 x )}{2} = \frac{1}{2}

化简

sin (4 x) = \frac{1}{2}

sin (4 x) = \frac{1}{2}

sin (4 x) = \frac{1}{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}

4 x = \frac{π}{6} + 2 πn, 4 x = \frac{5 π}{6} + 2 πn

4 x = \frac{π}{6} + 2 πn, 4 x = \frac{5 π}{6} + 2 πn

解

4 x = \frac{π}{6} + 2 πn : x = \frac{π}{24} + \frac{πn}{2}

4 x = \frac{π}{6} + 2 πn

两边除以

4

4 x = \frac{π}{6} + 2 πn

两边除以

4

\frac{4 x}{4} = \frac{\frac{π}{6}}{4} + \frac{2 πn}{4}

化简

\frac{4 x}{4} = \frac{\frac{π}{6}}{4} + \frac{2 πn}{4}

化简

\frac{4 x}{4} : x

\frac{4 x}{4}

数字相除:

\frac{4}{4} = 1

= x

化简

\frac{\frac{π}{6}}{4} + \frac{2 πn}{4} : \frac{π}{24} + \frac{πn}{2}

\frac{\frac{π}{6}}{4} + \frac{2 πn}{4}

\frac{\frac{π}{6}}{4} = \frac{π}{24}

\frac{\frac{π}{6}}{4}

使用分式法则:

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

= \frac{π}{6 \cdot 4}

数字相乘:

6 \cdot 4 = 24

= \frac{π}{24}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

约分:

2

= \frac{πn}{2}

= \frac{π}{24} + \frac{πn}{2}

x = \frac{π}{24} + \frac{πn}{2}

x = \frac{π}{24} + \frac{πn}{2}

x = \frac{π}{24} + \frac{πn}{2}

解

4 x = \frac{5 π}{6} + 2 πn : x = \frac{5 π}{24} + \frac{πn}{2}

4 x = \frac{5 π}{6} + 2 πn

两边除以

4

4 x = \frac{5 π}{6} + 2 πn

两边除以

4

\frac{4 x}{4} = \frac{\frac{5 π}{6}}{4} + \frac{2 πn}{4}

化简

\frac{4 x}{4} = \frac{\frac{5 π}{6}}{4} + \frac{2 πn}{4}

化简

\frac{4 x}{4} : x

\frac{4 x}{4}

数字相除:

\frac{4}{4} = 1

= x

化简

\frac{\frac{5 π}{6}}{4} + \frac{2 πn}{4} : \frac{5 π}{24} + \frac{πn}{2}

\frac{\frac{5 π}{6}}{4} + \frac{2 πn}{4}

\frac{\frac{5 π}{6}}{4} = \frac{5 π}{24}

\frac{\frac{5 π}{6}}{4}

使用分式法则:

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

= \frac{5 π}{6 \cdot 4}

数字相乘:

6 \cdot 4 = 24

= \frac{5 π}{24}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

约分:

2

= \frac{πn}{2}

= \frac{5 π}{24} + \frac{πn}{2}

x = \frac{5 π}{24} + \frac{πn}{2}

x = \frac{5 π}{24} + \frac{πn}{2}

x = \frac{5 π}{24} + \frac{πn}{2}

x = \frac{π}{24} + \frac{πn}{2}, x = \frac{5 π}{24} + \frac{πn}{2}

在

- 2 π \leq x \leq 3 π

范围内的解

x = \frac{π}{24}, x = \frac{5 π}{24}, x = \frac{13 π}{24}, x = \frac{17 π}{24}, x = \frac{25 π}{24}, x = \frac{29 π}{24}, x = \frac{37 π}{24}, x = \frac{41 π}{24}, x = \frac{49 π}{24}, x = \frac{53 π}{24}, x = - \frac{11 π}{24}, x = - \frac{7 π}{24}, x = - \frac{23 π}{24}, x = - \frac{19 π}{24}, x = - \frac{35 π}{24}, x = - \frac{31 π}{24}, x = - \frac{47 π}{24}, x = - \frac{43 π}{24}

作图

流行的例子

tan (θ) = \frac{10}{10}

0=sin(θ/2)-sin(θ)

0 = sin (\frac{θ}{2}) - sin (θ)

sin (b) = 0.823

(29)/(sin(50))=(37)/(sin(x))

\frac{29}{sin ( 5 0 ^{\circ} )} = \frac{37}{sin ( x )}

arccos (θ) = 1.6