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^2(x)+sqrt(3)tan(x)=0,0<= x<360

解答

tan^{2} (x) + 3 tan (x) = 0, 0^{\circ} \leq x < 36 0^{\circ}

解答

x = 0, x = 18 0^{\circ}, x = 12 0^{\circ}, x = 30 0^{\circ}

+1

弧度

x = 0, x = π, x = \frac{2 π}{3}, x = \frac{5 π}{3}

求解步骤

tan^{2} (x) + 3 tan (x) = 0, 0^{\circ} \leq x < 36 0^{\circ}

用替代法求解

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

令

: tan (x) = u

u^{2} + 3 u = 0

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

u^{2} + 3 u = 0

使用求根公式求解

u^{2} + 3 u = 0

二次方程求根公式:

若

a = 1, b = 3, c = 0

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

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

(3)^{2} - 4 \cdot 1 \cdot 0 = 3

(3)^{2} - 4 \cdot 1 \cdot 0

(3)^{2} = 3

(3)^{2}

使用根式运算法则:

a = a^{\frac{1}{2}}

= (3^{\frac{1}{2}})^{2}

使用指数法则:

(a^{b})^{c} = a^{b c}

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

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

分式相乘:

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

= \frac{1 \cdot 2}{2}

约分:

2

= 1

= 3

4 \cdot 1 \cdot 0 = 0

4 \cdot 1 \cdot 0

使用法则

0 \cdot a = 0

= 0

= 3 - 0

数字相减:

3 - 0 = 3

= 3

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

将解分隔开

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

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

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

同类项相加:

- 3 + 3 = 0

= \frac{0}{2 \cdot 1}

数字相乘:

2 \cdot 1 = 2

= \frac{0}{2}

使用法则

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

= 0

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

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

同类项相加:

- 3 - 3 = - 23

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

数字相乘:

2 \cdot 1 = 2

= \frac{- 2 3}{2}

使用分式法则:

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

= - \frac{2 3}{2}

数字相除:

\frac{2}{2} = 1

= - 3

二次方程组的解是:

u = 0, u = - 3

u = tan (x)

代回

tan (x) = 0, tan (x) = - 3

tan (x) = 0, tan (x) = - 3

tan (x) = 0, 0 \leq x < 36 0^{\circ} : x = 0, x = 18 0^{\circ}

tan (x) = 0, 0 \leq x < 36 0^{\circ}

tan (x) = 0

的通解

tan (x)

周期表（周期为

18 0^{\circ} n

）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

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

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

解

x = 0 + 18 0^{\circ} n : x = 18 0^{\circ} n

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

0 + 18 0^{\circ} n = 18 0^{\circ} n

x = 18 0^{\circ} n

x = 18 0^{\circ} n

在

0 \leq x < 36 0^{\circ}

范围内的解

x = 0, x = 18 0^{\circ}

tan (x) = - 3, 0 \leq x < 36 0^{\circ} : x = 12 0^{\circ}, x = 30 0^{\circ}

tan (x) = - 3, 0 \leq x < 36 0^{\circ}

tan (x) = - 3

的通解

tan (x)

周期表（周期为

18 0^{\circ} n

）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = 12 0^{\circ} + 18 0^{\circ} n

x = 12 0^{\circ} + 18 0^{\circ} n

在

0 \leq x < 36 0^{\circ}

范围内的解

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

合并所有解

x = 0, x = 18 0^{\circ}, x = 12 0^{\circ}, x = 30 0^{\circ}

作图

流行的例子

1/2 (6.50941)+cos(θ)(10.40478)=12

\frac{1}{2} (6.50941) + cos (θ) (10.40478) = 12

- 8 = - 4 + 4 tan (θ)

cos (x) = 0.2588

2tan^2(x)+3tan(x)+1=0

2 tan^{2} (x) + 3 tan (x) + 1 = 0

-arctan(t)=(4-pi)/4

- arctan (t) = \frac{4 - π}{4}