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受欢迎的三角函数 >

sqrt(3)tan(2x)=-1

解答

3 tan (2 x) = - 1

解答

x = \frac{5 π}{12} + \frac{πn}{2}

+1

度数

x = 7 5^{\circ} + 9 0^{\circ} n

求解步骤

3 tan (2 x) = - 1

两边除以

3

3 tan (2 x) = - 1

两边除以

3

\frac{3 tan ( 2 x )}{3} = \frac{- 1}{3}

化简

\frac{3 tan ( 2 x )}{3} = \frac{- 1}{3}

化简

\frac{3 tan ( 2 x )}{3} : tan (2 x)

\frac{3 tan ( 2 x )}{3}

约分:

3

= tan (2 x)

化简

\frac{- 1}{3} : - \frac{3}{3}

\frac{- 1}{3}

使用分式法则:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{1}{3}

- \frac{1}{3}

有理化:

- \frac{3}{3}

- \frac{1}{3}

乘以共轭根式

\frac{3}{3}

= - \frac{1 \cdot 3}{3 3}

1 \cdot 3 = 3

33 = 3

33

使用根式运算法则:

a a = a

33 = 3

= 3

= - \frac{3}{3}

= - \frac{3}{3}

tan (2 x) = - \frac{3}{3}

tan (2 x) = - \frac{3}{3}

tan (2 x) = - \frac{3}{3}

tan (2 x) = - \frac{3}{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}

2 x = \frac{5 π}{6} + πn

2 x = \frac{5 π}{6} + πn

解

2 x = \frac{5 π}{6} + πn : x = \frac{5 π}{12} + \frac{πn}{2}

2 x = \frac{5 π}{6} + πn

两边除以

2

2 x = \frac{5 π}{6} + πn

两边除以

2

\frac{2 x}{2} = \frac{\frac{5 π}{6}}{2} + \frac{πn}{2}

化简

\frac{2 x}{2} = \frac{\frac{5 π}{6}}{2} + \frac{πn}{2}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

\frac{\frac{5 π}{6}}{2} + \frac{πn}{2} : \frac{5 π}{12} + \frac{πn}{2}

\frac{\frac{5 π}{6}}{2} + \frac{πn}{2}

\frac{\frac{5 π}{6}}{2} = \frac{5 π}{12}

\frac{\frac{5 π}{6}}{2}

使用分式法则:

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

= \frac{5 π}{6 \cdot 2}

数字相乘:

6 \cdot 2 = 12

= \frac{5 π}{12}

= \frac{5 π}{12} + \frac{πn}{2}

x = \frac{5 π}{12} + \frac{πn}{2}

x = \frac{5 π}{12} + \frac{πn}{2}

x = \frac{5 π}{12} + \frac{πn}{2}

x = \frac{5 π}{12} + \frac{πn}{2}

作图

流行的例子

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

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}