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 >

4sin(2x)-sqrt(12)=0,0<= x<= 2pi

解答

4 sin (2 x) - 12 = 0, 0 \leq x \leq 2 π

解答

x = \frac{π}{6}, x = \frac{π}{3}, x = \frac{7 π}{6}, x = \frac{4 π}{3}

+1

度数

x = 3 0^{\circ}, x = 6 0^{\circ}, x = 21 0^{\circ}, x = 24 0^{\circ}

求解步骤

4 sin (2 x) - 12 = 0, 0 \leq x \leq 2 π

12 = 23

12

12

质因数分解:

2^{2} \cdot 3

12

12

除以

212 = 6 \cdot 2

= 2 \cdot 6

6

除以

26 = 3 \cdot 2

= 2 \cdot 2 \cdot 3

2, 3

都是质数，因此无法进一步因数分解

= 2 \cdot 2 \cdot 3

= 2^{2} \cdot 3

= 2^{2} \cdot 3

使用根式运算法则:

n ab = n a n b

= 3 2^{2}

使用根式运算法则:

n a^{n} = a

2^{2} = 2

= 23

4 sin (2 x) - 23 = 0

将

23

到右边

4 sin (2 x) - 23 = 0

两边加上

23

4 sin (2 x) - 23 + 23 = 0 + 23

化简

4 sin (2 x) = 23

4 sin (2 x) = 23

两边除以

4

4 sin (2 x) = 23

两边除以

4

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

化简

sin (2 x) = \frac{3}{2}

sin (2 x) = \frac{3}{2}

sin (2 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}

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

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

解

2 x = \frac{π}{3} + 2 πn : x = \frac{π}{6} + πn

2 x = \frac{π}{3} + 2 πn

两边除以

2

2 x = \frac{π}{3} + 2 πn

两边除以

2

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

化简

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

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

\frac{\frac{π}{3}}{2} + \frac{2 πn}{2} : \frac{π}{6} + πn

\frac{\frac{π}{3}}{2} + \frac{2 πn}{2}

\frac{\frac{π}{3}}{2} = \frac{π}{6}

\frac{\frac{π}{3}}{2}

使用分式法则:

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

= \frac{π}{3 \cdot 2}

数字相乘:

3 \cdot 2 = 6

= \frac{π}{6}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数字相除:

\frac{2}{2} = 1

= πn

= \frac{π}{6} + πn

x = \frac{π}{6} + πn

x = \frac{π}{6} + πn

x = \frac{π}{6} + πn

解

2 x = \frac{2 π}{3} + 2 πn : x = \frac{π}{3} + πn

2 x = \frac{2 π}{3} + 2 πn

两边除以

2

2 x = \frac{2 π}{3} + 2 πn

两边除以

2

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

化简

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

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

\frac{\frac{2 π}{3}}{2} + \frac{2 πn}{2} : \frac{π}{3} + πn

\frac{\frac{2 π}{3}}{2} + \frac{2 πn}{2}

\frac{\frac{2 π}{3}}{2} = \frac{π}{3}

\frac{\frac{2 π}{3}}{2}

使用分式法则:

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

= \frac{2 π}{3 \cdot 2}

数字相乘:

3 \cdot 2 = 6

= \frac{2 π}{6}

约分:

2

= \frac{π}{3}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数字相除:

\frac{2}{2} = 1

= πn

= \frac{π}{3} + πn

x = \frac{π}{3} + πn

x = \frac{π}{3} + πn

x = \frac{π}{3} + πn

x = \frac{π}{6} + πn, x = \frac{π}{3} + πn

在

0 \leq x \leq 2 π

范围内的解

x = \frac{π}{6}, x = \frac{π}{3}, x = \frac{7 π}{6}, x = \frac{4 π}{3}

作图

流行的例子

1*10^6=(400*cos(θ)+700)^2+(400*sin(θ))^2

1 \cdot 1 0^{6} = (400 \cdot cos (θ) + 700)^{2} + (400 \cdot sin (θ))^{2}

sin(x)-0.5*cos(x)=0.768

sin (x) - 0.5 \cdot cos (x) = 0.768

sin(x/2)= 1/2 ,0<= ,x<= 360

sin (\frac{x}{2}) = \frac{1}{2}, 0 \leq, x \leq 36 0^{\circ}

tan (x) = \frac{4}{10}

solvefor x,sin(y/x)+cos(x/y)=0

so l v e f or x, sin (\frac{y}{x}) + cos (\frac{x}{y}) = 0