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受欢迎的三角函数 >

cot^3(x)+cot(x)=0

解答

cot^{3} (x) + cot (x) = 0

解答

x = \frac{π}{2} + πn

+1

度数

x = 9 0^{\circ} + 18 0^{\circ} n

求解步骤

cot^{3} (x) + cot (x) = 0

用替代法求解

cot^{3} (x) + cot (x) = 0

令

: cot (x) = u

u^{3} + u = 0

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

u^{3} + u = 0

因式分解

u^{3} + u : u (u^{2} + 1)

u^{3} + u

使用指数法则:

a^{b + c} = a^{b} a^{c}

u^{3} = u^{2} u

= u^{2} u + u

因式分解出通项

u

= u (u^{2} + 1)

u (u^{2} + 1) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

u = 0 or u^{2} + 1 = 0

解

u^{2} + 1 = 0 : u = i, u = - i

u^{2} + 1 = 0

将

1

到右边

u^{2} + 1 = 0

两边减去

1

u^{2} + 1 - 1 = 0 - 1

化简

u^{2} = - 1

u^{2} = - 1

对于

x^{2} = f (a)

解为

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

u = - 1, u = - - 1

化简

- 1 : i

- 1

使用虚数运算法则:

- 1 = i

= i

化简

- - 1 : - i

- - 1

使用虚数运算法则:

- 1 = i

= - i

u = i, u = - i

解为

u = 0, u = i, u = - i

u = cot (x)

代回

cot (x) = 0, cot (x) = i, cot (x) = - i

cot (x) = 0, cot (x) = i, cot (x) = - i

cot (x) = 0 : x = \frac{π}{2} + πn

cot (x) = 0

cot (x) = 0

的通解

cot (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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{π}{2} + πn

x = \frac{π}{2} + πn

cot (x) = i :

无解

cot (x) = i

无解

cot (x) = - i :

无解

cot (x) = - i

无解

合并所有解

x = \frac{π}{2} + πn

作图

流行的例子

21+18cos(x)=16(1-cos^2(x))

sin(2a+10)=cos(3a-20)

b= 3/((cot(x)))

4sin^2(x)+cos(x)+1=0

(cot^2(x))-csc(x)=1