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受欢迎的三角函数 >

tan^2(3x)=1

解答

tan^{2} (3 x) = 1

解答

x = \frac{π}{12} + \frac{πn}{3}, x = \frac{π}{4} + \frac{πn}{3}

+1

度数

x = 1 5^{\circ} + 6 0^{\circ} n, x = 4 5^{\circ} + 6 0^{\circ} n

求解步骤

tan^{2} (3 x) = 1

用替代法求解

tan^{2} (3 x) = 1

令

: tan (3 x) = u

u^{2} = 1

u^{2} = 1 : u = 1, u = - 1

u^{2} = 1

对于

x^{2} = f (a)

解为

x = f (a), - f (a)

u = 1, u = - 1

1 = 1

1

使用法则

1 = 1

= 1

- 1 = - 1

- 1

使用法则

1 = 1

= - 1

u = 1, u = - 1

u = tan (3 x)

代回

tan (3 x) = 1, tan (3 x) = - 1

tan (3 x) = 1, tan (3 x) = - 1

tan (3 x) = 1 : x = \frac{π}{12} + \frac{πn}{3}

tan (3 x) = 1

tan (3 x) = 1

的通解

tan (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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

3 x = \frac{π}{4} + πn

3 x = \frac{π}{4} + πn

解

3 x = \frac{π}{4} + πn : x = \frac{π}{12} + \frac{πn}{3}

3 x = \frac{π}{4} + πn

两边除以

3

3 x = \frac{π}{4} + πn

两边除以

3

\frac{3 x}{3} = \frac{\frac{π}{4}}{3} + \frac{πn}{3}

化简

\frac{3 x}{3} = \frac{\frac{π}{4}}{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}{4}}{3} + \frac{πn}{3} : \frac{π}{12} + \frac{πn}{3}

\frac{\frac{π}{4}}{3} + \frac{πn}{3}

\frac{\frac{π}{4}}{3} = \frac{π}{12}

\frac{\frac{π}{4}}{3}

使用分式法则:

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

= \frac{π}{4 \cdot 3}

数字相乘:

4 \cdot 3 = 12

= \frac{π}{12}

= \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}

tan (3 x) = - 1 : x = \frac{π}{4} + \frac{πn}{3}

tan (3 x) = - 1

tan (3 x) = - 1

的通解

tan (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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

3 x = \frac{3 π}{4} + πn

3 x = \frac{3 π}{4} + πn

解

3 x = \frac{3 π}{4} + πn : x = \frac{π}{4} + \frac{πn}{3}

3 x = \frac{3 π}{4} + πn

两边除以

3

3 x = \frac{3 π}{4} + πn

两边除以

3

\frac{3 x}{3} = \frac{\frac{3 π}{4}}{3} + \frac{πn}{3}

化简

\frac{3 x}{3} = \frac{\frac{3 π}{4}}{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{3 π}{4}}{3} + \frac{πn}{3} : \frac{π}{4} + \frac{πn}{3}

\frac{\frac{3 π}{4}}{3} + \frac{πn}{3}

\frac{\frac{3 π}{4}}{3} = \frac{π}{4}

\frac{\frac{3 π}{4}}{3}

使用分式法则:

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

= \frac{3 π}{4 \cdot 3}

数字相乘:

4 \cdot 3 = 12

= \frac{3 π}{12}

约分:

3

= \frac{π}{4}

= \frac{π}{4} + \frac{πn}{3}

x = \frac{π}{4} + \frac{πn}{3}

x = \frac{π}{4} + \frac{πn}{3}

x = \frac{π}{4} + \frac{πn}{3}

x = \frac{π}{4} + \frac{πn}{3}

合并所有解

x = \frac{π}{12} + \frac{πn}{3}, x = \frac{π}{4} + \frac{πn}{3}

作图

流行的例子

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