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受欢迎的三角函数 >

cos((2x+3)/2)=-1/2

解答

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

解答

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

+1

度数

x = 34.05633 \dots^{\circ} + 36 0^{\circ} n, x = 154.05633 \dots^{\circ} + 36 0^{\circ} n

求解步骤

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

cos (\frac{2 x + 3}{2}) = - \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{2 x + 3}{2} = \frac{2 π}{3} + 2 πn, \frac{2 x + 3}{2} = \frac{4 π}{3} + 2 πn

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

解

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

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

在两边乘以

2

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

在两边乘以

2

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

化简

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

化简

\frac{2 ( 2 x + 3 )}{2} : 2 x + 3

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

数字相除:

\frac{2}{2} = 1

= 2 x + 3

化简

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

2 \cdot \frac{2 π}{3} + 2 \cdot 2 πn

2 \cdot \frac{2 π}{3} = \frac{4 π}{3}

2 \cdot \frac{2 π}{3}

分式相乘:

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

= \frac{2 π 2}{3}

数字相乘:

2 \cdot 2 = 4

= \frac{4 π}{3}

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

数字相乘:

2 \cdot 2 = 4

= 4 πn

= \frac{4 π}{3} + 4 πn

2 x + 3 = \frac{4 π}{3} + 4 πn

2 x + 3 = \frac{4 π}{3} + 4 πn

2 x + 3 = \frac{4 π}{3} + 4 πn

将

3

到右边

2 x + 3 = \frac{4 π}{3} + 4 πn

两边减去

3

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

化简

2 x = \frac{4 π}{3} + 4 πn - 3

2 x = \frac{4 π}{3} + 4 πn - 3

两边除以

2

2 x = \frac{4 π}{3} + 4 πn - 3

两边除以

2

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

化简

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

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

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

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

对同类项分组

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

\frac{4 πn}{2} = 2 πn

\frac{4 πn}{2}

数字相除:

\frac{4}{2} = 2

= 2 πn

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

\frac{\frac{4 π}{3}}{2}

使用分式法则:

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

= \frac{4 π}{3 \cdot 2}

数字相乘:

3 \cdot 2 = 6

= \frac{4 π}{6}

约分:

2

= \frac{2 π}{3}

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

对同类项分组

= 2 πn - \frac{3}{2} + \frac{2 π}{3}

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

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

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

解

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

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

在两边乘以

2

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

在两边乘以

2

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

化简

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

化简

\frac{2 ( 2 x + 3 )}{2} : 2 x + 3

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

数字相除:

\frac{2}{2} = 1

= 2 x + 3

化简

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

2 \cdot \frac{4 π}{3} + 2 \cdot 2 πn

2 \cdot \frac{4 π}{3} = \frac{8 π}{3}

2 \cdot \frac{4 π}{3}

分式相乘:

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

= \frac{4 π 2}{3}

数字相乘:

4 \cdot 2 = 8

= \frac{8 π}{3}

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

数字相乘:

2 \cdot 2 = 4

= 4 πn

= \frac{8 π}{3} + 4 πn

2 x + 3 = \frac{8 π}{3} + 4 πn

2 x + 3 = \frac{8 π}{3} + 4 πn

2 x + 3 = \frac{8 π}{3} + 4 πn

将

3

到右边

2 x + 3 = \frac{8 π}{3} + 4 πn

两边减去

3

2 x + 3 - 3 = \frac{8 π}{3} + 4 πn - 3

化简

2 x = \frac{8 π}{3} + 4 πn - 3

2 x = \frac{8 π}{3} + 4 πn - 3

两边除以

2

2 x = \frac{8 π}{3} + 4 πn - 3

两边除以

2

\frac{2 x}{2} = \frac{\frac{8 π}{3}}{2} + \frac{4 πn}{2} - \frac{3}{2}

化简

\frac{2 x}{2} = \frac{\frac{8 π}{3}}{2} + \frac{4 πn}{2} - \frac{3}{2}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

\frac{\frac{8 π}{3}}{2} + \frac{4 πn}{2} - \frac{3}{2} : 2 πn - \frac{3}{2} + \frac{4 π}{3}

\frac{\frac{8 π}{3}}{2} + \frac{4 πn}{2} - \frac{3}{2}

对同类项分组

= - \frac{3}{2} + \frac{4 πn}{2} + \frac{\frac{8 π}{3}}{2}

\frac{4 πn}{2} = 2 πn

\frac{4 πn}{2}

数字相除:

\frac{4}{2} = 2

= 2 πn

\frac{\frac{8 π}{3}}{2} = \frac{4 π}{3}

\frac{\frac{8 π}{3}}{2}

使用分式法则:

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

= \frac{8 π}{3 \cdot 2}

数字相乘:

3 \cdot 2 = 6

= \frac{8 π}{6}

约分:

2

= \frac{4 π}{3}

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

对同类项分组

= 2 πn - \frac{3}{2} + \frac{4 π}{3}

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

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

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

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

作图

流行的例子

1=cot^2(x)+csc(x)

1 = cot^{2} (x) + csc (x)

sin(θ/2)=(sqrt(3))/2

sin (\frac{θ}{2}) = \frac{3}{2}

cos (θ) = - 2

cos (x) = - \frac{π}{3}

tan(θ)=-sqrt(2)sin(θ)

tan (θ) = - 2 sin (θ)