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受欢迎的三角函数 >

6cot^2(x)-18=0

解答

6 cot^{2} (x) - 18 = 0

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

6 cot^{2} (x) - 18 = 0

用替代法求解

6 cot^{2} (x) - 18 = 0

令

: cot (x) = u

6 u^{2} - 18 = 0

6 u^{2} - 18 = 0 : u = 3, u = - 3

6 u^{2} - 18 = 0

将

18

到右边

6 u^{2} - 18 = 0

两边加上

18

6 u^{2} - 18 + 18 = 0 + 18

化简

6 u^{2} = 18

6 u^{2} = 18

两边除以

6

6 u^{2} = 18

两边除以

6

\frac{6 u ^{2}}{6} = \frac{18}{6}

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

20sin^2(x)+cos(x)-19=0

tan^2(x)=2-tan(x)

cos(7x)(2cos(x)+1)=0

sin(3x+pi/(18))=1