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受欢迎的三角函数 >

2cos((3x-pi)/6)+1=0,0<x<2pi

解答

2 cos (\frac{3 x - π}{6}) + 1 = 0, 0 < x < 2 π

解答

x = \frac{5 π}{3}

+1

度数

x = 30 0^{\circ}

求解步骤

2 cos (\frac{3 x - π}{6}) + 1 = 0, 0 < x < 2 π

将

1

到右边

2 cos (\frac{3 x - π}{6}) + 1 = 0

两边减去

1

2 cos (\frac{3 x - π}{6}) + 1 - 1 = 0 - 1

化简

2 cos (\frac{3 x - π}{6}) = - 1

2 cos (\frac{3 x - π}{6}) = - 1

两边除以

2

2 cos (\frac{3 x - π}{6}) = - 1

两边除以

2

\frac{2 cos ( \frac{3 x - π}{6} )}{2} = \frac{- 1}{2}

化简

cos (\frac{3 x - π}{6}) = - \frac{1}{2}

cos (\frac{3 x - π}{6}) = - \frac{1}{2}

cos (\frac{3 x - π}{6}) = - \frac{1}{2}

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}

\frac{3 x - π}{6} = \frac{2 π}{3} + 2 πn, \frac{3 x - π}{6} = \frac{4 π}{3} + 2 πn

\frac{3 x - π}{6} = \frac{2 π}{3} + 2 πn, \frac{3 x - π}{6} = \frac{4 π}{3} + 2 πn

解

\frac{3 x - π}{6} = \frac{2 π}{3} + 2 πn : x = \frac{5 π}{3} + 4 πn

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

在两边乘以

6

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

在两边乘以

6

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

化简

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

化简

\frac{6 ( 3 x - π )}{6} : 3 x - π

\frac{6 ( 3 x - π )}{6}

数字相除:

\frac{6}{6} = 1

= 3 x - π

化简

6 \cdot \frac{2 π}{3} + 6 \cdot 2 πn : 4 π + 12 πn

6 \cdot \frac{2 π}{3} + 6 \cdot 2 πn

6 \cdot \frac{2 π}{3} = 4 π

6 \cdot \frac{2 π}{3}

分式相乘:

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

= \frac{2 π 6}{3}

数字相乘:

2 \cdot 6 = 12

= \frac{12 π}{3}

数字相除:

\frac{12}{3} = 4

= 4 π

6 \cdot 2 πn = 12 πn

6 \cdot 2 πn

数字相乘:

6 \cdot 2 = 12

= 12 πn

= 4 π + 12 πn

3 x - π = 4 π + 12 πn

3 x - π = 4 π + 12 πn

3 x - π = 4 π + 12 πn

将

π

到右边

3 x - π = 4 π + 12 πn

两边加上

π

3 x - π + π = 4 π + 12 πn + π

化简

3 x = 5 π + 12 πn

3 x = 5 π + 12 πn

两边除以

3

3 x = 5 π + 12 πn

两边除以

3

\frac{3 x}{3} = \frac{5 π}{3} + \frac{12 πn}{3}

化简

x = \frac{5 π}{3} + 4 πn

x = \frac{5 π}{3} + 4 πn

解

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

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

在两边乘以

6

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

在两边乘以

6

\frac{6 ( 3 x - π )}{6} = 6 \cdot \frac{4 π}{3} + 6 \cdot 2 πn

化简

\frac{6 ( 3 x - π )}{6} = 6 \cdot \frac{4 π}{3} + 6 \cdot 2 πn

化简

\frac{6 ( 3 x - π )}{6} : 3 x - π

\frac{6 ( 3 x - π )}{6}

数字相除:

\frac{6}{6} = 1

= 3 x - π

化简

6 \cdot \frac{4 π}{3} + 6 \cdot 2 πn : 8 π + 12 πn

6 \cdot \frac{4 π}{3} + 6 \cdot 2 πn

6 \cdot \frac{4 π}{3} = 8 π

6 \cdot \frac{4 π}{3}

分式相乘:

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

= \frac{4 π 6}{3}

数字相乘:

4 \cdot 6 = 24

= \frac{24 π}{3}

数字相除:

\frac{24}{3} = 8

= 8 π

6 \cdot 2 πn = 12 πn

6 \cdot 2 πn

数字相乘:

6 \cdot 2 = 12

= 12 πn

= 8 π + 12 πn

3 x - π = 8 π + 12 πn

3 x - π = 8 π + 12 πn

3 x - π = 8 π + 12 πn

将

π

到右边

3 x - π = 8 π + 12 πn

两边加上

π

3 x - π + π = 8 π + 12 πn + π

化简

3 x = 9 π + 12 πn

3 x = 9 π + 12 πn

两边除以

3

3 x = 9 π + 12 πn

两边除以

3

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

化简

\frac{3 x}{3} = \frac{9 π}{3} + \frac{12 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{9 π}{3} + \frac{12 πn}{3} : 3 π + 4 πn

\frac{9 π}{3} + \frac{12 πn}{3}

数字相除:

\frac{9}{3} = 3

= 3 π + \frac{12 πn}{3}

数字相除:

\frac{12}{3} = 4

= 3 π + 4 πn

x = 3 π + 4 πn

x = 3 π + 4 πn

x = 3 π + 4 πn

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

在

0 < x < 2 π

范围内的解

x = \frac{5 π}{3}

作图

流行的例子

2cos^2(a)+cos(a)-1=0

2 cos^{2} (a) + cos (a) - 1 = 0

arctan(e^x)= pi/4

arctan (e^{x}) = \frac{π}{4}

2cos^2(2x)+3cos(2x)-2=0

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

tan(t)=-12/5 ,(3pi)/2 <t<2pi

tan (t) = - \frac{12}{5}, \frac{3 π}{2} < t < 2 π

3sin(x)+5cos(x)=4

3 sin (x) + 5 cos (x) = 4