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受欢迎的三角函数 >

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

解答

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

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

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

分解

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

sec (x) csc (x) - 2 csc (x)

因式分解出通项

csc (x)

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

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

csc(3θ)=6sin(3θ),0<θ<2pi

csc (3 θ) = 6 sin (3 θ), 0 < θ < 2 π

sqrt(3)tan(3θ)-1=0,0<= θ<= 2pi

3 tan (3 θ) - 1 = 0, 0 \leq θ \leq 2 π

(cot(θ)+1)(csc(θ)-1)=0

(cot (θ) + 1) (csc (θ) - 1) = 0

2sin(x)cos(x)=1

2 sin (x) cos (x) = 1

cos(x)sin(x)+2sin(x)=0

cos (x) sin (x) + 2 sin (x) = 0