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受欢迎的三角函数 >

sqrt(3)sec(x)csc(x)=2csc(x)

解答

3 sec (x) csc (x) = 2 csc (x)

解答

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

+1

度数

x = 3 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n

求解步骤

3 sec (x) csc (x) = 2 csc (x)

两边减去

2 csc (x)

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

分解

3 sec (x) csc (x) - 2 csc (x) : csc (x) (3 sec (x) - 2)

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

因式分解出通项

csc (x)

= csc (x) (3 sec (x) - 2)

csc (x) (3 sec (x) - 2) = 0

分别求解每个部分

csc (x) = 0 or 3 sec (x) - 2 = 0

csc (x) = 0 :

无解

csc (x) = 0

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

无解

3 sec (x) - 2 = 0 : x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

3 sec (x) - 2 = 0

将

2

到右边

3 sec (x) - 2 = 0

两边加上

2

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

化简

3 sec (x) = 2

3 sec (x) = 2

两边除以

3

3 sec (x) = 2

两边除以

3

\frac{3 sec ( x )}{3} = \frac{2}{3}

化简

\frac{3 sec ( x )}{3} = \frac{2}{3}

化简

\frac{3 sec ( x )}{3} : sec (x)

\frac{3 sec ( x )}{3}

约分:

3

= sec (x)

化简

\frac{2}{3} : \frac{2 3}{3}

\frac{2}{3}

乘以共轭根式

\frac{3}{3}

= \frac{2 3}{3 3}

33 = 3

33

使用根式运算法则:

a a = a

33 = 3

= 3

= \frac{2 3}{3}

sec (x) = \frac{2 3}{3}

sec (x) = \frac{2 3}{3}

sec (x) = \frac{2 3}{3}

sec (x) = \frac{2 3}{3}

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}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

合并所有解

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

作图

流行的例子

(2sin(x)-1)(2cos(x)-sqrt(3))=0

(2 sin (x) - 1) (2 cos (x) - 3) = 0

cos (θ) = - \frac{6}{7}

sec(θ)=-sqrt(5)

sec (θ) = - 5

sin(2x)-sqrt(3)cos(x)=0

sin (2 x) - 3 cos (x) = 0

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

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