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受欢迎的三角函数 >

3cot^2(x)=sqrt(3)cot(x)

解答

3 cot^{2} (x) = 3 cot (x)

解答

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

+1

度数

x = 9 0^{\circ} + 18 0^{\circ} n, x = 6 0^{\circ} + 18 0^{\circ} n

求解步骤

3 cot^{2} (x) = 3 cot (x)

用替代法求解

3 cot^{2} (x) = 3 cot (x)

令

: cot (x) = u

3 u^{2} = 3 u

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

3 u^{2} = 3 u

将

3 u

para o lado esquerdo

3 u^{2} = 3 u

两边减去

3 u

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

化简

3 u^{2} - 3 u = 0

3 u^{2} - 3 u = 0

因式分解

3 u^{2} - 3 u : u (3 u - 3)

3 u^{2} - 3 u

使用指数法则:

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

u^{2} = uu

= 3 uu - 3 u

因式分解出通项

u

= u (3 u - 1 \cdot 3)

数字相乘:

1 \cdot 3 = 3

= u (3 u - 3)

u (3 u - 3) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

u = 0 or 3 u - 3 = 0

解

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

3 u - 3 = 0

将

3

到右边

3 u - 3 = 0

两边加上

3

3 u - 3 + 3 = 0 + 3

化简

3 u = 3

3 u = 3

两边除以

3

3 u = 3

两边除以

3

\frac{3 u}{3} = \frac{3}{3}

化简

u = \frac{3}{3}

u = \frac{3}{3}

二次方程组的解是:

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

u = cot (x)

代回

cot (x) = 0, cot (x) = \frac{3}{3}

cot (x) = 0, cot (x) = \frac{3}{3}

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) = \frac{3}{3} : x = \frac{π}{3} + πn

cot (x) = \frac{3}{3}

cot (x) = \frac{3}{3}

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}{3} + πn

x = \frac{π}{3} + πn

合并所有解

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

作图

流行的例子

sin(7x)=(sqrt(3))/2

sin (7 x) = \frac{3}{2}

-1.9sin(t)=0.4cos(2t)

- 1.9 sin (t) = 0.4 cos (2 t)

sin(x/2)=(sqrt(2))/2

sin (\frac{x}{2}) = \frac{2}{2}

sin (2 t) = 1

sin^4(x)=sin^2(x)

sin^{4} (x) = sin^{2} (x)