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受欢迎的三角函数 >

sqrt(3)csc(x)+csc(x)cot(x)=0

解答

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

解答

x = \frac{5 π}{6} + πn

+1

度数

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

求解步骤

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

分解

3 csc (x) + csc (x) cot (x) : csc (x) (3 + cot (x))

3 csc (x) + csc (x) cot (x)

因式分解出通项

csc (x)

= csc (x) (3 + cot (x))

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

分别求解每个部分

csc (x) = 0 or 3 + cot (x) = 0

csc (x) = 0 :

无解

csc (x) = 0

csc (x) \leq - 1 or csc (x) \geq 1

无解

3 + cot (x) = 0 : x = \frac{5 π}{6} + πn

3 + cot (x) = 0

将

3

到右边

3 + cot (x) = 0

两边减去

3

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

化简

cot (x) = - 3

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{5 π}{6} + πn

作图

流行的例子

-3cos^2(θ)-10cos(θ)=-3cos(θ)-6

- 3 cos^{2} (θ) - 10 cos (θ) = - 3 cos (θ) - 6

-4sin(x)=-cos^2(x)+4

- 4 sin (x) = - cos^{2} (x) + 4

sin^2(x)-4sin(x)+3=0

sin^{2} (x) - 4 sin (x) + 3 = 0

6sin(x)+csc(x)=0

6 sin (x) + csc (x) = 0

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

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