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受欢迎的三角函数 >

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

解答

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

解答

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

+1

度数

x = 3 0^{\circ} + 18 0^{\circ} n, x = 9 0^{\circ} + 18 0^{\circ} n

求解步骤

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

cos (2 x + \frac{π}{3}) = - \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}

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

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

解

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

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

将

\frac{π}{3}

到右边

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

两边减去

\frac{π}{3}

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

化简

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

化简

2 x + \frac{π}{3} - \frac{π}{3} : 2 x

2 x + \frac{π}{3} - \frac{π}{3}

同类项相加:

\frac{π}{3} - \frac{π}{3} = 0

= 2 x

化简

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

\frac{2 π}{3} + 2 πn - \frac{π}{3}

对同类项分组

= 2 πn - \frac{π}{3} + \frac{2 π}{3}

合并分式

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

使用法则

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

= \frac{- π + 2 π}{3}

同类项相加:

- π + 2 π = π

= \frac{π}{3}

= 2 πn + \frac{π}{3}

2 x = 2 πn + \frac{π}{3}

2 x = 2 πn + \frac{π}{3}

2 x = 2 πn + \frac{π}{3}

两边除以

2

2 x = 2 πn + \frac{π}{3}

两边除以

2

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

化简

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

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

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数字相除:

\frac{2}{2} = 1

= πn

\frac{\frac{π}{3}}{2} = \frac{π}{6}

\frac{\frac{π}{3}}{2}

使用分式法则:

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

= \frac{π}{3 \cdot 2}

数字相乘:

3 \cdot 2 = 6

= \frac{π}{6}

= πn + \frac{π}{6}

x = πn + \frac{π}{6}

x = πn + \frac{π}{6}

x = πn + \frac{π}{6}

解

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

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

将

\frac{π}{3}

到右边

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

两边减去

\frac{π}{3}

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

化简

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

化简

2 x + \frac{π}{3} - \frac{π}{3} : 2 x

2 x + \frac{π}{3} - \frac{π}{3}

同类项相加:

\frac{π}{3} - \frac{π}{3} = 0

= 2 x

化简

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

\frac{4 π}{3} + 2 πn - \frac{π}{3}

对同类项分组

= 2 πn - \frac{π}{3} + \frac{4 π}{3}

合并分式

- \frac{π}{3} + \frac{4 π}{3} : π

使用法则

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

= \frac{- π + 4 π}{3}

同类项相加:

- π + 4 π = 3 π

= \frac{3 π}{3}

数字相除:

\frac{3}{3} = 1

= π

= 2 πn + π

2 x = 2 πn + π

2 x = 2 πn + π

2 x = 2 πn + π

两边除以

2

2 x = 2 πn + π

两边除以

2

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

化简

x = πn + \frac{π}{2}

x = πn + \frac{π}{2}

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

作图

流行的例子

sec(θ+20)=sqrt(3)

sec (θ + 2 0^{\circ}) = 3

tan(θ)=(7.7)/(14)

tan (θ) = \frac{7.7}{14}

cos(x)=(sqrt(3))/3

cos (x) = \frac{3}{3}

3 + 4 cos (θ) = - 1

cot(x)tan(x)=sec(x)csc(x)

cot (x) tan (x) = sec (x) csc (x)