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受欢迎的三角函数 >

cos(2x+3)=0

解答

cos (2 x + 3) = 0

解答

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

+1

度数

x = - 40.94366 \dots^{\circ} + 18 0^{\circ} n, x = 49.05633 \dots^{\circ} + 18 0^{\circ} n

求解步骤

cos (2 x + 3) = 0

cos (2 x + 3) = 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}

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

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

解

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

2 x + 3 = \frac{π}{2} + 2 πn

将

3

到右边

2 x + 3 = \frac{π}{2} + 2 πn

两边减去

3

2 x + 3 - 3 = \frac{π}{2} + 2 πn - 3

化简

2 x = \frac{π}{2} + 2 πn - 3

2 x = \frac{π}{2} + 2 πn - 3

两边除以

2

2 x = \frac{π}{2} + 2 πn - 3

两边除以

2

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

化简

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

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

对同类项分组

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

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数字相除:

\frac{2}{2} = 1

= πn

\frac{\frac{π}{2}}{2} = \frac{π}{4}

\frac{\frac{π}{2}}{2}

使用分式法则:

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

= \frac{π}{2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

= \frac{π}{4}

= - \frac{3}{2} + πn + \frac{π}{4}

对同类项分组

= πn - \frac{3}{2} + \frac{π}{4}

x = πn - \frac{3}{2} + \frac{π}{4}

x = πn - \frac{3}{2} + \frac{π}{4}

x = πn - \frac{3}{2} + \frac{π}{4}

解

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

2 x + 3 = \frac{3 π}{2} + 2 πn

将

3

到右边

2 x + 3 = \frac{3 π}{2} + 2 πn

两边减去

3

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

化简

2 x = \frac{3 π}{2} + 2 πn - 3

2 x = \frac{3 π}{2} + 2 πn - 3

两边除以

2

2 x = \frac{3 π}{2} + 2 πn - 3

两边除以

2

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

化简

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

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

对同类项分组

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

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数字相除:

\frac{2}{2} = 1

= πn

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

\frac{\frac{3 π}{2}}{2}

使用分式法则:

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

= \frac{3 π}{2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

= \frac{3 π}{4}

= - \frac{3}{2} + πn + \frac{3 π}{4}

对同类项分组

= πn - \frac{3}{2} + \frac{3 π}{4}

x = πn - \frac{3}{2} + \frac{3 π}{4}

x = πn - \frac{3}{2} + \frac{3 π}{4}

x = πn - \frac{3}{2} + \frac{3 π}{4}

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

作图

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