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受欢迎的三角函数 >

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

解答

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

解答

x = \frac{π}{18} + \frac{2 πn}{3}, x = \frac{11 π}{18} + \frac{2 πn}{3}

+1

弧度

x = \frac{π}{18} + \frac{2 π}{3} n, x = \frac{11 π}{18} + \frac{2 π}{3} n

求解步骤

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

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

sec (3 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}

3 x = \frac{π}{6} + 2 πn, 3 x = \frac{11 π}{6} + 2 πn

3 x = \frac{π}{6} + 2 πn, 3 x = \frac{11 π}{6} + 2 πn

解

3 x = \frac{π}{6} + 2 πn : x = \frac{π}{18} + \frac{2 πn}{3}

3 x = \frac{π}{6} + 2 πn

两边除以

3

3 x = \frac{π}{6} + 2 πn

两边除以

3

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

化简

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

化简

\frac{3 x}{3} : x

\frac{3 x}{3}

数字相除:

\frac{3}{3} = 1

= x

化简

\frac{\frac{π}{6}}{3} + \frac{2 πn}{3} : \frac{π}{18} + \frac{2 πn}{3}

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

\frac{\frac{π}{6}}{3} = \frac{π}{18}

\frac{\frac{π}{6}}{3}

使用分式法则:

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

= \frac{π}{6 \cdot 3}

数字相乘:

6 \cdot 3 = 18

= \frac{π}{18}

= \frac{π}{18} + \frac{2 πn}{3}

x = \frac{π}{18} + \frac{2 πn}{3}

x = \frac{π}{18} + \frac{2 πn}{3}

x = \frac{π}{18} + \frac{2 πn}{3}

解

3 x = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{18} + \frac{2 πn}{3}

3 x = \frac{11 π}{6} + 2 πn

两边除以

3

3 x = \frac{11 π}{6} + 2 πn

两边除以

3

\frac{3 x}{3} = \frac{\frac{11 π}{6}}{3} + \frac{2 πn}{3}

化简

\frac{3 x}{3} = \frac{\frac{11 π}{6}}{3} + \frac{2 πn}{3}

化简

\frac{3 x}{3} : x

\frac{3 x}{3}

数字相除:

\frac{3}{3} = 1

= x

化简

\frac{\frac{11 π}{6}}{3} + \frac{2 πn}{3} : \frac{11 π}{18} + \frac{2 πn}{3}

\frac{\frac{11 π}{6}}{3} + \frac{2 πn}{3}

\frac{\frac{11 π}{6}}{3} = \frac{11 π}{18}

\frac{\frac{11 π}{6}}{3}

使用分式法则:

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

= \frac{11 π}{6 \cdot 3}

数字相乘:

6 \cdot 3 = 18

= \frac{11 π}{18}

= \frac{11 π}{18} + \frac{2 πn}{3}

x = \frac{11 π}{18} + \frac{2 πn}{3}

x = \frac{11 π}{18} + \frac{2 πn}{3}

x = \frac{11 π}{18} + \frac{2 πn}{3}

x = \frac{π}{18} + \frac{2 πn}{3}, x = \frac{11 π}{18} + \frac{2 πn}{3}

作图

流行的例子

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3sin^2(x)-5sin(x)+2=0

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tan (\frac{1}{2} x) + 3 = 0