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受欢迎的三角函数 >

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

解答

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

解答

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

+1

度数

x = 3 0^{\circ} + 18 0^{\circ} n, x = 15 0^{\circ} + 18 0^{\circ} n

求解步骤

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

用替代法求解

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

令

: cot (x) = u

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

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

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

将

3

到右边

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

两边减去

3

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

化简

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

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

将

u^{2}

para o lado esquerdo

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

两边加上

u^{2}

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

化简

- u^{2} = - 3

- u^{2} = - 3

两边除以

- 1

- u^{2} = - 3

两边除以

- 1

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

化简

u^{2} = 3

u^{2} = 3

对于

x^{2} = f (a)

解为

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

u = 3, u = - 3

u = cot (x)

代回

cot (x) = 3, cot (x) = - 3

cot (x) = 3, cot (x) = - 3

cot (x) = 3 : x = \frac{π}{6} + πn

cot (x) = 3

cot (x) = 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}{6} + πn

x = \frac{π}{6} + πn

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

cot (x) = - 3

cot (x) = - 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{5 π}{6} + πn

x = \frac{5 π}{6} + πn

合并所有解

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

作图

流行的例子

2 cos (t) + 1 = 0

sin(3x)= 1/(sqrt(2))

sin (3 x) = \frac{1}{2}

sec(θ)=-2/(sqrt(3))

sec (θ) = - \frac{2}{3}

tan (θ) = \frac{8}{12}

0 = cos (3 x)