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受欢迎的三角函数 >

6sec(x)csc(x)=12csc(x)

解答

6 sec (x) csc (x) = 12 csc (x)

解答

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

+1

度数

x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

求解步骤

6 sec (x) csc (x) = 12 csc (x)

两边减去

12 csc (x)

6 sec (x) csc (x) - 12 csc (x) = 0

分解

6 sec (x) csc (x) - 12 csc (x) : 6 csc (x) (sec (x) - 2)

6 sec (x) csc (x) - 12 csc (x)

将

- 12

改写为

2 \cdot 6

= 6 sec (x) csc (x) + 2 \cdot 6 csc (x)

因式分解出通项

6 csc (x)

= 6 csc (x) (sec (x) - 2)

6 csc (x) (sec (x) - 2) = 0

分别求解每个部分

csc (x) = 0 or sec (x) - 2 = 0

csc (x) = 0 :

无解

csc (x) = 0

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

无解

sec (x) - 2 = 0 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

sec (x) - 2 = 0

将

2

到右边

sec (x) - 2 = 0

两边加上

2

sec (x) - 2 + 2 = 0 + 2

化简

sec (x) = 2

sec (x) = 2

sec (x) = 2

的通解

sec (x)

周期表（周期为

2 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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

合并所有解

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

作图

流行的例子

2tan^2(θ)+3tan(θ)=0

2 tan^{2} (θ) + 3 tan (θ) = 0

tan(x)+cot(x)=2

tan (x) + cot (x) = 2

4cos^2(x)-4sin(x)-5=0

4 cos^{2} (x) - 4 sin (x) - 5 = 0

solvefor x,tan(x^2+y^2)=1

so l v e f or x, tan (x^{2} + y^{2}) = 1

2tan(x)+sec(x)=0

2 tan (x) + sec (x) = 0