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受欢迎的三角函数 >

cos(3x-9x)=0

解答

cos (3 x - 9 x) = 0

解答

x = - \frac{π}{12} - \frac{πn}{3}, x = - \frac{π}{4} - \frac{πn}{3}

+1

度数

x = - 1 5^{\circ} - 6 0^{\circ} n, x = - 4 5^{\circ} - 6 0^{\circ} n

求解步骤

cos (3 x - 9 x) = 0

cos (3 x - 9 x) = 0

的通解

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} 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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

3 x - 9 x = \frac{π}{2} + 2 πn, 3 x - 9 x = \frac{3 π}{2} + 2 πn

3 x - 9 x = \frac{π}{2} + 2 πn, 3 x - 9 x = \frac{3 π}{2} + 2 πn

解

3 x - 9 x = \frac{π}{2} + 2 πn : x = - \frac{π}{12} - \frac{πn}{3}

3 x - 9 x = \frac{π}{2} + 2 πn

同类项相加:

3 x - 9 x = - 6 x

- 6 x = \frac{π}{2} + 2 πn

两边除以

- 6

- 6 x = \frac{π}{2} + 2 πn

两边除以

- 6

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

化简

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

化简

\frac{- 6 x}{- 6} : x

\frac{- 6 x}{- 6}

使用分式法则:

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

= \frac{6 x}{6}

数字相除:

\frac{6}{6} = 1

= x

化简

\frac{\frac{π}{2}}{- 6} + \frac{2 πn}{- 6} : - \frac{π}{12} - \frac{πn}{3}

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

\frac{\frac{π}{2}}{- 6} = - \frac{π}{12}

\frac{\frac{π}{2}}{- 6}

使用分式法则:

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

= - \frac{\frac{π}{2}}{6}

使用分式法则:

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

\frac{\frac{π}{2}}{6} = \frac{π}{2 \cdot 6}

= - \frac{π}{2 \cdot 6}

数字相乘:

2 \cdot 6 = 12

= - \frac{π}{12}

= - \frac{π}{12} + \frac{2 πn}{- 6}

\frac{2 πn}{- 6} = - \frac{πn}{3}

\frac{2 πn}{- 6}

使用分式法则:

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

= - \frac{2 πn}{6}

约分:

2

= - \frac{πn}{3}

= - \frac{π}{12} - \frac{πn}{3}

x = - \frac{π}{12} - \frac{πn}{3}

x = - \frac{π}{12} - \frac{πn}{3}

x = - \frac{π}{12} - \frac{πn}{3}

解

3 x - 9 x = \frac{3 π}{2} + 2 πn : x = - \frac{π}{4} - \frac{πn}{3}

3 x - 9 x = \frac{3 π}{2} + 2 πn

同类项相加:

3 x - 9 x = - 6 x

- 6 x = \frac{3 π}{2} + 2 πn

两边除以

- 6

- 6 x = \frac{3 π}{2} + 2 πn

两边除以

- 6

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

化简

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

化简

\frac{- 6 x}{- 6} : x

\frac{- 6 x}{- 6}

使用分式法则:

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

= \frac{6 x}{6}

数字相除:

\frac{6}{6} = 1

= x

化简

\frac{\frac{3 π}{2}}{- 6} + \frac{2 πn}{- 6} : - \frac{π}{4} - \frac{πn}{3}

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

\frac{\frac{3 π}{2}}{- 6} = - \frac{π}{4}

\frac{\frac{3 π}{2}}{- 6}

使用分式法则:

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

= - \frac{\frac{3 π}{2}}{6}

使用分式法则:

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

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

= - \frac{3 π}{2 \cdot 6}

数字相乘:

2 \cdot 6 = 12

= - \frac{3 π}{12}

约分:

3

= - \frac{π}{4}

= - \frac{π}{4} + \frac{2 πn}{- 6}

\frac{2 πn}{- 6} = - \frac{πn}{3}

\frac{2 πn}{- 6}

使用分式法则:

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

= - \frac{2 πn}{6}

约分:

2

= - \frac{πn}{3}

= - \frac{π}{4} - \frac{πn}{3}

x = - \frac{π}{4} - \frac{πn}{3}

x = - \frac{π}{4} - \frac{πn}{3}

x = - \frac{π}{4} - \frac{πn}{3}

x = - \frac{π}{12} - \frac{πn}{3}, x = - \frac{π}{4} - \frac{πn}{3}

作图

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