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受欢迎的三角函数 >

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

解答

cot (3 x) = \frac{3}{3}, 0 \leq x \leq 2 π

解答

x = \frac{π}{9}, x = \frac{4 π}{9}, x = \frac{7 π}{9}, x = \frac{10 π}{9}, x = \frac{13 π}{9}

+1

度数

x = 2 0^{\circ}, x = 8 0^{\circ}, x = 14 0^{\circ}, x = 20 0^{\circ}, x = 26 0^{\circ}

求解步骤

cot (3 x) = \frac{3}{3}, 0 \leq x \leq 2 π

cot (3 x) = \frac{3}{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{π}{3} + πn

3 x = \frac{π}{3} + πn

解

3 x = \frac{π}{3} + πn : x = \frac{π}{9} + \frac{πn}{3}

3 x = \frac{π}{3} + πn

两边除以

3

3 x = \frac{π}{3} + πn

两边除以

3

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

化简

\frac{3 x}{3} = \frac{\frac{π}{3}}{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{π}{3}}{3} + \frac{πn}{3} : \frac{π}{9} + \frac{πn}{3}

\frac{\frac{π}{3}}{3} + \frac{πn}{3}

\frac{\frac{π}{3}}{3} = \frac{π}{9}

\frac{\frac{π}{3}}{3}

使用分式法则:

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

= \frac{π}{3 \cdot 3}

数字相乘:

3 \cdot 3 = 9

= \frac{π}{9}

= \frac{π}{9} + \frac{πn}{3}

x = \frac{π}{9} + \frac{πn}{3}

x = \frac{π}{9} + \frac{πn}{3}

x = \frac{π}{9} + \frac{πn}{3}

x = \frac{π}{9} + \frac{πn}{3}

在

0 \leq x \leq 2 π

范围内的解

x = \frac{π}{9}, x = \frac{4 π}{9}, x = \frac{7 π}{9}, x = \frac{10 π}{9}, x = \frac{13 π}{9}

作图

流行的例子

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