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 >

3tan^2(3x)=1

解答

3 tan^{2} (3 x) = 1

解答

x = \frac{π}{18} + \frac{πn}{3}, x = - \frac{π}{18} + \frac{πn}{3}

+1

度数

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

求解步骤

3 tan^{2} (3 x) = 1

用替代法求解

3 tan^{2} (3 x) = 1

令

: tan (3 x) = u

3 u^{2} = 1

3 u^{2} = 1 : u = \frac{1}{3}, u = - \frac{1}{3}

3 u^{2} = 1

两边除以

3

3 u^{2} = 1

两边除以

3

\frac{3 u ^{2}}{3} = \frac{1}{3}

化简

u^{2} = \frac{1}{3}

u^{2} = \frac{1}{3}

对于

x^{2} = f (a)

解为

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

u = \frac{1}{3}, u = - \frac{1}{3}

u = tan (3 x)

代回

tan (3 x) = \frac{1}{3}, tan (3 x) = - \frac{1}{3}

tan (3 x) = \frac{1}{3}, tan (3 x) = - \frac{1}{3}

tan (3 x) = \frac{1}{3} : x = \frac{π}{18} + \frac{πn}{3}

tan (3 x) = \frac{1}{3}

使用反三角函数性质

tan (3 x) = \frac{1}{3}

tan (3 x) = \frac{1}{3}

的通解

tan (x) = a \Rightarrow x = arctan (a) + πn

3 x = arctan (\frac{1}{3}) + πn

3 x = arctan (\frac{1}{3}) + πn

解

3 x = arctan (\frac{1}{3}) + πn : x = \frac{π}{18} + \frac{πn}{3}

3 x = arctan (\frac{1}{3}) + πn

化简

arctan (\frac{1}{3}) + πn : \frac{π}{6} + πn

arctan (\frac{1}{3}) + πn

使用以下普通恒等式:

arctan (\frac{1}{3}) = \frac{π}{6}

x 0 \frac{3}{3} 13 arctan (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} arctan (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ}

= \frac{π}{6} + πn

3 x = \frac{π}{6} + πn

两边除以

3

3 x = \frac{π}{6} + πn

两边除以

3

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

化简

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

\frac{\frac{π}{6}}{3} + \frac{πn}{3}

\frac{\frac{π}{6}}{3} = \frac{π}{18}

\frac{\frac{π}{6}}{3}

使用分式法则:

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

= \frac{π}{6 \cdot 3}

数字相乘:

6 \cdot 3 = 18

= \frac{π}{18}

= \frac{π}{18} + \frac{πn}{3}

x = \frac{π}{18} + \frac{πn}{3}

x = \frac{π}{18} + \frac{πn}{3}

x = \frac{π}{18} + \frac{πn}{3}

x = \frac{π}{18} + \frac{πn}{3}

tan (3 x) = - \frac{1}{3} : x = - \frac{π}{18} + \frac{πn}{3}

tan (3 x) = - \frac{1}{3}

使用反三角函数性质

tan (3 x) = - \frac{1}{3}

tan (3 x) = - \frac{1}{3}

的通解

tan (x) = - a \Rightarrow x = arctan (- a) + πn

3 x = arctan (- \frac{1}{3}) + πn

3 x = arctan (- \frac{1}{3}) + πn

解

3 x = arctan (- \frac{1}{3}) + πn : x = - \frac{π}{18} + \frac{πn}{3}

3 x = arctan (- \frac{1}{3}) + πn

化简

arctan (- \frac{1}{3}) + πn : - \frac{π}{6} + πn

arctan (- \frac{1}{3}) + πn

arctan (- \frac{1}{3}) = - \frac{π}{6}

arctan (- \frac{1}{3})

利用以下特性:

arctan (- x) = - arctan (x)

arctan (- \frac{1}{3}) = - arctan (\frac{1}{3})

= - arctan (\frac{1}{3})

使用以下普通恒等式:

arctan (\frac{1}{3}) = \frac{π}{6}

arctan (\frac{1}{3})

x 0 \frac{3}{3} 13 arctan (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} arctan (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ}

= \frac{π}{6}

= - \frac{π}{6}

= - \frac{π}{6} + πn

3 x = - \frac{π}{6} + πn

两边除以

3

3 x = - \frac{π}{6} + πn

两边除以

3

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

化简

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

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

\frac{\frac{π}{6}}{3} = \frac{π}{18}

\frac{\frac{π}{6}}{3}

使用分式法则:

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

= \frac{π}{6 \cdot 3}

数字相乘:

6 \cdot 3 = 18

= \frac{π}{18}

= - \frac{π}{18} + \frac{πn}{3}

x = - \frac{π}{18} + \frac{πn}{3}

x = - \frac{π}{18} + \frac{πn}{3}

x = - \frac{π}{18} + \frac{πn}{3}

x = - \frac{π}{18} + \frac{πn}{3}

合并所有解

x = \frac{π}{18} + \frac{πn}{3}, x = - \frac{π}{18} + \frac{πn}{3}

作图

流行的例子

6tan(x)-5csc(x)=0

6 tan (x) - 5 csc (x) = 0

3csc(x)-6=0,0<= x<= 360

3 csc (x) - 6 = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

-sec^2(x)+1=-5sec(x)-5

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

tan^2(x)+4tan(x)+3=0

tan^{2} (x) + 4 tan (x) + 3 = 0

(1+tan(x))^2+(1-tan(x))^2=sec^2(x)

(1 + tan (x))^{2} + (1 - tan (x))^{2} = sec^{2} (x)