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受欢迎的三角函数 >

sqrt(3)csc(2x)+2=0

解答

3 csc (2 x) + 2 = 0

解答

x = \frac{2 π}{3} + πn, x = \frac{5 π}{6} + πn

+1

度数

x = 12 0^{\circ} + 18 0^{\circ} n, x = 15 0^{\circ} + 18 0^{\circ} n

求解步骤

3 csc (2 x) + 2 = 0

将

2

到右边

3 csc (2 x) + 2 = 0

两边减去

2

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

化简

3 csc (2 x) = - 2

3 csc (2 x) = - 2

两边除以

3

3 csc (2 x) = - 2

两边除以

3

\frac{3 csc ( 2 x )}{3} = \frac{- 2}{3}

化简

\frac{3 csc ( 2 x )}{3} = \frac{- 2}{3}

化简

\frac{3 csc ( 2 x )}{3} : csc (2 x)

\frac{3 csc ( 2 x )}{3}

约分:

3

= csc (2 x)

化简

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

\frac{- 2}{3}

使用分式法则:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{2}{3}

- \frac{2}{3}

有理化:

- \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}

= - \frac{2 3}{3}

csc (2 x) = - \frac{2 3}{3}

csc (2 x) = - \frac{2 3}{3}

csc (2 x) = - \frac{2 3}{3}

csc (2 x) = - \frac{2 3}{3}

的通解

csc (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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 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} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

2 x = \frac{4 π}{3} + 2 πn, 2 x = \frac{5 π}{3} + 2 πn

2 x = \frac{4 π}{3} + 2 πn, 2 x = \frac{5 π}{3} + 2 πn

解

2 x = \frac{4 π}{3} + 2 πn : x = \frac{2 π}{3} + πn

2 x = \frac{4 π}{3} + 2 πn

两边除以

2

2 x = \frac{4 π}{3} + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{\frac{4 π}{3}}{2} + \frac{2 πn}{2}

化简

\frac{2 x}{2} = \frac{\frac{4 π}{3}}{2} + \frac{2 πn}{2}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

\frac{\frac{4 π}{3}}{2} + \frac{2 πn}{2} : \frac{2 π}{3} + πn

\frac{\frac{4 π}{3}}{2} + \frac{2 πn}{2}

\frac{\frac{4 π}{3}}{2} = \frac{2 π}{3}

\frac{\frac{4 π}{3}}{2}

使用分式法则:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{4 π}{3 \cdot 2}

数字相乘:

3 \cdot 2 = 6

= \frac{4 π}{6}

约分:

2

= \frac{2 π}{3}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数字相除:

\frac{2}{2} = 1

= πn

= \frac{2 π}{3} + πn

x = \frac{2 π}{3} + πn

x = \frac{2 π}{3} + πn

x = \frac{2 π}{3} + πn

解

2 x = \frac{5 π}{3} + 2 πn : x = \frac{5 π}{6} + πn

2 x = \frac{5 π}{3} + 2 πn

两边除以

2

2 x = \frac{5 π}{3} + 2 πn

两边除以

2

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

化简

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

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

\frac{\frac{5 π}{3}}{2} + \frac{2 πn}{2} : \frac{5 π}{6} + πn

\frac{\frac{5 π}{3}}{2} + \frac{2 πn}{2}

\frac{\frac{5 π}{3}}{2} = \frac{5 π}{6}

\frac{\frac{5 π}{3}}{2}

使用分式法则:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{5 π}{3 \cdot 2}

数字相乘:

3 \cdot 2 = 6

= \frac{5 π}{6}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数字相除:

\frac{2}{2} = 1

= πn

= \frac{5 π}{6} + πn

x = \frac{5 π}{6} + πn

x = \frac{5 π}{6} + πn

x = \frac{5 π}{6} + πn

x = \frac{2 π}{3} + πn, x = \frac{5 π}{6} + πn

作图

流行的例子

- 25 sin (5 x) = 0

6sin^2(x)-sin(x)-1=0

6 sin^{2} (x) - sin (x) - 1 = 0

sin (x) = \frac{9}{11}

sec^{2} (x) = - 4

0 = 2 sin (x) + 1