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^4(x)-9=0

解答

tan^{4} (x) - 9 = 0

解答

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

+1

度数

x = 6 0^{\circ} + 18 0^{\circ} n, x = 12 0^{\circ} + 18 0^{\circ} n

求解步骤

tan^{4} (x) - 9 = 0

用替代法求解

tan^{4} (x) - 9 = 0

令

: tan (x) = u

u^{4} - 9 = 0

u^{4} - 9 = 0 : u = 3, u = - 3, u = 3 i, u = - 3 i

u^{4} - 9 = 0

将

9

到右边

u^{4} - 9 = 0

两边加上

9

u^{4} - 9 + 9 = 0 + 9

化简

u^{4} = 9

u^{4} = 9

用

v = u^{2}

和

v^{2} = u^{4}

改写方程式

v^{2} = 9

解

v^{2} = 9 : v = 9, v = - 9

v^{2} = 9

对于

(g (x))^{2} = f (a)

解为

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

v = 9, v = - 9

v = 9, v = - 9

代回

v = u^{2}

，求解

u

解

u^{2} = 9 : u = 3, u = - 3

u^{2} = 9

化简

9 : 3

9

因式分解数字:

9 = 3^{2}

= 3^{2}

使用根式运算法则:

n a^{n} = a

3^{2} = 3

= 3

对于

x^{2} = f (a)

解为

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

u = 3, u = - 3

解

u^{2} = - 9 : u = 3 i, u = - 3 i

u^{2} = - 9

9 = 3

9

因式分解数字:

9 = 3^{2}

= 3^{2}

使用根式运算法则:

n a^{n} = a

3^{2} = 3

= 3

u^{2} = - 3

对于

x^{2} = f (a)

解为

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

u = - 3, u = - - 3

化简

- 3 : 3 i

- 3

使用根式运算法则:

- a = - 1 a

- 3 = - 1 3

= - 1 3

使用虚数运算法则:

- 1 = i

= 3 i

化简

- - 3 : - 3 i

- - 3

化简

- 3 : 3 i

- 3

使用根式运算法则:

- a = - 1 a

- 3 = - 1 3

= - 1 3

使用虚数运算法则:

- 1 = i

= 3 i

= - 3 i

u = 3 i, u = - 3 i

解为

u = 3, u = - 3, u = 3 i, u = - 3 i

u = tan (x)

代回

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

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

tan (x) = 3 : x = \frac{π}{3} + πn

tan (x) = 3

tan (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}

x = \frac{π}{3} + πn

x = \frac{π}{3} + πn

tan (x) = - 3 : x = \frac{2 π}{3} + πn

tan (x) = - 3

tan (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}

x = \frac{2 π}{3} + πn

x = \frac{2 π}{3} + πn

tan (x) = 3 i :

无解

tan (x) = 3 i

无解

tan (x) = - 3 i :

无解

tan (x) = - 3 i

无解

合并所有解

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

作图

流行的例子

(tan(x)-1)(sqrt(3)cot(x)-1)=0

(tan (x) - 1) (3 cot (x) - 1) = 0

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

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

3sin(x)=7cos(x)

3 sin (x) = 7 cos (x)

8 sin (θ) - 3 = 0

cos^2(4x)-sin^2(4x)=cos(b)

cos^{2} (4 x) - sin^{2} (4 x) = cos (b)