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 >

cot(3x)=-sqrt(3),0<= x<= 2pi

解答

cot (3 x) = - 3, 0 \leq x \leq 2 π

解答

x = \frac{5 π}{18}, x = \frac{11 π}{18}, x = \frac{17 π}{18}, x = \frac{23 π}{18}, x = \frac{29 π}{18}

+1

度数

x = 5 0^{\circ}, x = 11 0^{\circ}, x = 17 0^{\circ}, x = 23 0^{\circ}, x = 29 0^{\circ}

求解步骤

cot (3 x) = - 3, 0 \leq x \leq 2 π

cot (3 x) = - 3

的通解

cot (x)

周期表（周期为

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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

3 x = \frac{5 π}{6} + πn

3 x = \frac{5 π}{6} + πn

解

3 x = \frac{5 π}{6} + πn : x = \frac{5 π}{18} + \frac{πn}{3}

3 x = \frac{5 π}{6} + πn

两边除以

3

3 x = \frac{5 π}{6} + πn

两边除以

3

\frac{3 x}{3} = \frac{\frac{5 π}{6}}{3} + \frac{πn}{3}

化简

\frac{3 x}{3} = \frac{\frac{5 π}{6}}{3} + \frac{πn}{3}

化简

\frac{3 x}{3} : x

\frac{3 x}{3}

数字相除:

\frac{3}{3} = 1

= x

化简

\frac{\frac{5 π}{6}}{3} + \frac{πn}{3} : \frac{5 π}{18} + \frac{πn}{3}

\frac{\frac{5 π}{6}}{3} + \frac{πn}{3}

\frac{\frac{5 π}{6}}{3} = \frac{5 π}{18}

\frac{\frac{5 π}{6}}{3}

使用分式法则:

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

= \frac{5 π}{6 \cdot 3}

数字相乘:

6 \cdot 3 = 18

= \frac{5 π}{18}

= \frac{5 π}{18} + \frac{πn}{3}

x = \frac{5 π}{18} + \frac{πn}{3}

x = \frac{5 π}{18} + \frac{πn}{3}

x = \frac{5 π}{18} + \frac{πn}{3}

x = \frac{5 π}{18} + \frac{πn}{3}

在

0 \leq x \leq 2 π

范围内的解

x = \frac{5 π}{18}, x = \frac{11 π}{18}, x = \frac{17 π}{18}, x = \frac{23 π}{18}, x = \frac{29 π}{18}

作图

流行的例子

3cos^2(x)+sin^2(x)=3

3 cos^{2} (x) + sin^{2} (x) = 3

4sin^2(x)+6sin(x)+2=0

4 sin^{2} (x) + 6 sin (x) + 2 = 0

sin^2(θ)+2-cos^2(θ)=3sin(θ)

sin^{2} (θ) + 2 - cos^{2} (θ) = 3 sin (θ)

sin(x)=sin^2(x)

sin (x) = sin^{2} (x)

sin^2(x)=cos^2(x)-1

sin^{2} (x) = cos^{2} (x) - 1