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 >

tan(2x)=sqrt(3),0<= x<2pi

解答

tan (2 x) = 3, 0 \leq x < 2 π

解答

x = \frac{π}{6}, x = \frac{2 π}{3}, x = \frac{7 π}{6}, x = \frac{5 π}{3}

+1

度数

x = 3 0^{\circ}, x = 12 0^{\circ}, x = 21 0^{\circ}, x = 30 0^{\circ}

求解步骤

tan (2 x) = 3, 0 \leq x < 2 π

tan (2 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}

2 x = \frac{π}{3} + πn

2 x = \frac{π}{3} + πn

解

2 x = \frac{π}{3} + πn : x = \frac{π}{6} + \frac{πn}{2}

2 x = \frac{π}{3} + πn

两边除以

2

2 x = \frac{π}{3} + πn

两边除以

2

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

化简

\frac{2 x}{2} = \frac{\frac{π}{3}}{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{π}{3}}{2} + \frac{πn}{2} : \frac{π}{6} + \frac{πn}{2}

\frac{\frac{π}{3}}{2} + \frac{πn}{2}

\frac{\frac{π}{3}}{2} = \frac{π}{6}

\frac{\frac{π}{3}}{2}

使用分式法则:

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

= \frac{π}{3 \cdot 2}

数字相乘:

3 \cdot 2 = 6

= \frac{π}{6}

= \frac{π}{6} + \frac{πn}{2}

x = \frac{π}{6} + \frac{πn}{2}

x = \frac{π}{6} + \frac{πn}{2}

x = \frac{π}{6} + \frac{πn}{2}

x = \frac{π}{6} + \frac{πn}{2}

在

0 \leq x < 2 π

范围内的解

x = \frac{π}{6}, x = \frac{2 π}{3}, x = \frac{7 π}{6}, x = \frac{5 π}{3}

作图

流行的例子

cos (0)

tan(arcsin(-3/5))

tan (arcsin (- \frac{3}{5}))

sec^{2} (x) - 2 = 0

cos(2t)=(-sqrt(3))/2

cos (2 t) = \frac{- 3}{2}

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

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