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受欢迎的三角函数 >

5cot^2(x)-15=0

解答

5 cot^{2} (x) - 15 = 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

5 cot^{2} (x) - 15 = 0

用替代法求解

5 cot^{2} (x) - 15 = 0

令

: cot (x) = u

5 u^{2} - 15 = 0

5 u^{2} - 15 = 0 : u = 3, u = - 3

5 u^{2} - 15 = 0

将

15

到右边

5 u^{2} - 15 = 0

两边加上

15

5 u^{2} - 15 + 15 = 0 + 15

化简

5 u^{2} = 15

5 u^{2} = 15

两边除以

5

5 u^{2} = 15

两边除以

5

\frac{5 u ^{2}}{5} = \frac{15}{5}

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

sin(x)= 2/(sqrt(5))

sin (x) = \frac{2}{5}

csc (x) = 5

sec^2(x)+tan^2(x)-1=0

sec^{2} (x) + tan^{2} (x) - 1 = 0

tan^2(x)-sqrt(3)tan(x)=0,0<= x<2pi

tan^{2} (x) - 3 tan (x) = 0, 0 \leq x < 2 π

tan (θ) = 10