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受欢迎的三角函数 >

sqrt(3)sec(8x)=2

解答

3 sec (8 x) = 2

解答

x = \frac{π}{48} + \frac{πn}{4}, x = \frac{11 π}{48} + \frac{πn}{4}

+1

度数

x = 3.7 5^{\circ} + 4 5^{\circ} n, x = 41.2 5^{\circ} + 4 5^{\circ} n

求解步骤

3 sec (8 x) = 2

两边除以

3

3 sec (8 x) = 2

两边除以

3

\frac{3 sec ( 8 x )}{3} = \frac{2}{3}

化简

\frac{3 sec ( 8 x )}{3} = \frac{2}{3}

化简

\frac{3 sec ( 8 x )}{3} : sec (8 x)

\frac{3 sec ( 8 x )}{3}

约分:

3

= sec (8 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 (8 x) = \frac{2 3}{3}

sec (8 x) = \frac{2 3}{3}

sec (8 x) = \frac{2 3}{3}

sec (8 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}

8 x = \frac{π}{6} + 2 πn, 8 x = \frac{11 π}{6} + 2 πn

8 x = \frac{π}{6} + 2 πn, 8 x = \frac{11 π}{6} + 2 πn

解

8 x = \frac{π}{6} + 2 πn : x = \frac{π}{48} + \frac{πn}{4}

8 x = \frac{π}{6} + 2 πn

两边除以

8

8 x = \frac{π}{6} + 2 πn

两边除以

8

\frac{8 x}{8} = \frac{\frac{π}{6}}{8} + \frac{2 πn}{8}

化简

\frac{8 x}{8} = \frac{\frac{π}{6}}{8} + \frac{2 πn}{8}

化简

\frac{8 x}{8} : x

\frac{8 x}{8}

数字相除:

\frac{8}{8} = 1

= x

化简

\frac{\frac{π}{6}}{8} + \frac{2 πn}{8} : \frac{π}{48} + \frac{πn}{4}

\frac{\frac{π}{6}}{8} + \frac{2 πn}{8}

\frac{\frac{π}{6}}{8} = \frac{π}{48}

\frac{\frac{π}{6}}{8}

使用分式法则:

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

= \frac{π}{6 \cdot 8}

数字相乘:

6 \cdot 8 = 48

= \frac{π}{48}

\frac{2 πn}{8} = \frac{πn}{4}

\frac{2 πn}{8}

约分:

2

= \frac{πn}{4}

= \frac{π}{48} + \frac{πn}{4}

x = \frac{π}{48} + \frac{πn}{4}

x = \frac{π}{48} + \frac{πn}{4}

x = \frac{π}{48} + \frac{πn}{4}

解

8 x = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{48} + \frac{πn}{4}

8 x = \frac{11 π}{6} + 2 πn

两边除以

8

8 x = \frac{11 π}{6} + 2 πn

两边除以

8

\frac{8 x}{8} = \frac{\frac{11 π}{6}}{8} + \frac{2 πn}{8}

化简

\frac{8 x}{8} = \frac{\frac{11 π}{6}}{8} + \frac{2 πn}{8}

化简

\frac{8 x}{8} : x

\frac{8 x}{8}

数字相除:

\frac{8}{8} = 1

= x

化简

\frac{\frac{11 π}{6}}{8} + \frac{2 πn}{8} : \frac{11 π}{48} + \frac{πn}{4}

\frac{\frac{11 π}{6}}{8} + \frac{2 πn}{8}

\frac{\frac{11 π}{6}}{8} = \frac{11 π}{48}

\frac{\frac{11 π}{6}}{8}

使用分式法则:

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

= \frac{11 π}{6 \cdot 8}

数字相乘:

6 \cdot 8 = 48

= \frac{11 π}{48}

\frac{2 πn}{8} = \frac{πn}{4}

\frac{2 πn}{8}

约分:

2

= \frac{πn}{4}

= \frac{11 π}{48} + \frac{πn}{4}

x = \frac{11 π}{48} + \frac{πn}{4}

x = \frac{11 π}{48} + \frac{πn}{4}

x = \frac{11 π}{48} + \frac{πn}{4}

x = \frac{π}{48} + \frac{πn}{4}, x = \frac{11 π}{48} + \frac{πn}{4}

作图

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