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 >

2tan^2(3x)=6

解答

2 tan^{2} (3 x) = 6

解答

x = \frac{π}{9} + \frac{πn}{3}, x = \frac{2 π}{9} + \frac{πn}{3}

+1

度数

x = 2 0^{\circ} + 6 0^{\circ} n, x = 4 0^{\circ} + 6 0^{\circ} n

求解步骤

2 tan^{2} (3 x) = 6

用替代法求解

2 tan^{2} (3 x) = 6

令

: tan (3 x) = u

2 u^{2} = 6

2 u^{2} = 6 : u = 3, u = - 3

2 u^{2} = 6

两边除以

2

2 u^{2} = 6

两边除以

2

\frac{2 u ^{2}}{2} = \frac{6}{2}

化简

u^{2} = 3

u^{2} = 3

对于

x^{2} = f (a)

解为

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

u = 3, u = - 3

u = tan (3 x)

代回

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

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

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

tan (3 x) = 3

tan (3 x) = 3

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}{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}

tan (3 x) = - 3 : x = \frac{2 π}{9} + \frac{πn}{3}

tan (3 x) = - 3

tan (3 x) = - 3

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{2 π}{3} + πn

3 x = \frac{2 π}{3} + πn

解

3 x = \frac{2 π}{3} + πn : x = \frac{2 π}{9} + \frac{πn}{3}

3 x = \frac{2 π}{3} + πn

两边除以

3

3 x = \frac{2 π}{3} + πn

两边除以

3

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

化简

\frac{3 x}{3} = \frac{\frac{2 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{2 π}{3}}{3} + \frac{πn}{3} : \frac{2 π}{9} + \frac{πn}{3}

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

\frac{\frac{2 π}{3}}{3} = \frac{2 π}{9}

\frac{\frac{2 π}{3}}{3}

使用分式法则:

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

= \frac{2 π}{3 \cdot 3}

数字相乘:

3 \cdot 3 = 9

= \frac{2 π}{9}

= \frac{2 π}{9} + \frac{πn}{3}

x = \frac{2 π}{9} + \frac{πn}{3}

x = \frac{2 π}{9} + \frac{πn}{3}

x = \frac{2 π}{9} + \frac{πn}{3}

x = \frac{2 π}{9} + \frac{πn}{3}

合并所有解

x = \frac{π}{9} + \frac{πn}{3}, x = \frac{2 π}{9} + \frac{πn}{3}

作图

流行的例子

5cos(x)+1=-2sin^2(x)

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

tan (x) = \frac{19}{11}

cot(x)=cot(3x-50),0<x<180

cot (x) = cot (3 x - 5 0^{\circ}), 0 < x < 18 0^{\circ}

tan (2 θ) = \frac{4}{3}

cos(θ)-1=cos(2θ)

cos (θ) - 1 = cos (2 θ)