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受欢迎的三角函数 >

cos(9x)=0

解答

cos (9 x) = 0

解答

x = \frac{π}{18} + \frac{2 πn}{9}, x = \frac{π}{6} + \frac{2 πn}{9}

+1

度数

x = 1 0^{\circ} + 4 0^{\circ} n, x = 3 0^{\circ} + 4 0^{\circ} n

求解步骤

cos (9 x) = 0

cos (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}

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

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

解

9 x = \frac{π}{2} + 2 πn : x = \frac{π}{18} + \frac{2 πn}{9}

9 x = \frac{π}{2} + 2 πn

两边除以

9

9 x = \frac{π}{2} + 2 πn

两边除以

9

\frac{9 x}{9} = \frac{\frac{π}{2}}{9} + \frac{2 πn}{9}

化简

\frac{9 x}{9} = \frac{\frac{π}{2}}{9} + \frac{2 πn}{9}

化简

\frac{9 x}{9} : x

\frac{9 x}{9}

数字相除:

\frac{9}{9} = 1

= x

化简

\frac{\frac{π}{2}}{9} + \frac{2 πn}{9} : \frac{π}{18} + \frac{2 πn}{9}

\frac{\frac{π}{2}}{9} + \frac{2 πn}{9}

\frac{\frac{π}{2}}{9} = \frac{π}{18}

\frac{\frac{π}{2}}{9}

使用分式法则:

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

= \frac{π}{2 \cdot 9}

数字相乘:

2 \cdot 9 = 18

= \frac{π}{18}

= \frac{π}{18} + \frac{2 πn}{9}

x = \frac{π}{18} + \frac{2 πn}{9}

x = \frac{π}{18} + \frac{2 πn}{9}

x = \frac{π}{18} + \frac{2 πn}{9}

解

9 x = \frac{3 π}{2} + 2 πn : x = \frac{π}{6} + \frac{2 πn}{9}

9 x = \frac{3 π}{2} + 2 πn

两边除以

9

9 x = \frac{3 π}{2} + 2 πn

两边除以

9

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

化简

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

化简

\frac{9 x}{9} : x

\frac{9 x}{9}

数字相除:

\frac{9}{9} = 1

= x

化简

\frac{\frac{3 π}{2}}{9} + \frac{2 πn}{9} : \frac{π}{6} + \frac{2 πn}{9}

\frac{\frac{3 π}{2}}{9} + \frac{2 πn}{9}

\frac{\frac{3 π}{2}}{9} = \frac{π}{6}

\frac{\frac{3 π}{2}}{9}

使用分式法则:

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

= \frac{3 π}{2 \cdot 9}

数字相乘:

2 \cdot 9 = 18

= \frac{3 π}{18}

约分:

3

= \frac{π}{6}

= \frac{π}{6} + \frac{2 πn}{9}

x = \frac{π}{6} + \frac{2 πn}{9}

x = \frac{π}{6} + \frac{2 πn}{9}

x = \frac{π}{6} + \frac{2 πn}{9}

x = \frac{π}{18} + \frac{2 πn}{9}, x = \frac{π}{6} + \frac{2 πn}{9}

作图

流行的例子

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2 cos^{3} (x) - 3 sin^{2} (x) cos (x) = 0

5 cot (θ) = - 6

cos (3 x - 9 x) = 0

7sin^2(θ)+15sin(θ)+8=0

7 sin^{2} (θ) + 15 sin (θ) + 8 = 0

2sin^{23}(x)+sin^{26}(x)-2=0

2 sin^{23} (x) + sin^{26} (x) - 2 = 0