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受欢迎的三角函数 >

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

解答

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

解答

x = πn, x = \frac{5 π}{6} + πn

+1

度数

x = 0^{\circ} + 18 0^{\circ} n, x = 15 0^{\circ} + 18 0^{\circ} n

求解步骤

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

用替代法求解

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

令

: tan (x) = u

3 u^{2} + u = 0

3 u^{2} + u = 0 : u = 0, u = - \frac{3}{3}

3 u^{2} + u = 0

使用求根公式求解

3 u^{2} + u = 0

二次方程求根公式:

若

a = 3, b = 1, c = 0

u_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 3 \cdot 0}{2 3}

u_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 3 \cdot 0}{2 3}

1^{2} - 43 \cdot 0 = 1

1^{2} - 43 \cdot 0

使用法则

1^{a} = 1

1^{2} = 1

= 1 - 4 \cdot 0 \cdot 3

使用法则

0 \cdot a = 0

= 1 - 0

数字相减:

1 - 0 = 1

= 1

使用法则

1 = 1

= 1

u_{1, 2} = \frac{- 1 \pm 1}{2 3}

将解分隔开

u_{1} = \frac{- 1 + 1}{2 3}, u_{2} = \frac{- 1 - 1}{2 3}

u = \frac{- 1 + 1}{2 3} : 0

\frac{- 1 + 1}{2 3}

数字相加/相减:

- 1 + 1 = 0

= \frac{0}{2 3}

使用法则

\frac{0}{a} = 0, a \neq = 0

= 0

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

\frac{- 1 - 1}{2 3}

数字相减:

- 1 - 1 = - 2

= \frac{- 2}{2 3}

使用分式法则:

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

= - \frac{2}{2 3}

数字相除:

\frac{2}{2} = 1

= - \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}

二次方程组的解是:

u = 0, u = - \frac{3}{3}

u = tan (x)

代回

tan (x) = 0, tan (x) = - \frac{3}{3}

tan (x) = 0, tan (x) = - \frac{3}{3}

tan (x) = 0 : x = πn

tan (x) = 0

tan (x) = 0

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}

x = 0 + πn

x = 0 + πn

解

x = 0 + πn : x = πn

x = 0 + πn

0 + πn = πn

x = πn

x = πn

tan (x) = - \frac{3}{3} : x = \frac{5 π}{6} + πn

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

tan (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}

x = \frac{5 π}{6} + πn

x = \frac{5 π}{6} + πn

合并所有解

x = πn, x = \frac{5 π}{6} + πn

作图

流行的例子

tan^2(x)-4sin(x)+4=0

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

1 - cos (2 x) = 0

sin (x) = \frac{37}{64}

15cos^2(x)+7cos(x)-2=0

15 cos^{2} (x) + 7 cos (x) - 2 = 0

2(sin(t))^2-sin(t)-1=0

2 (sin (t))^{2} - sin (t) - 1 = 0