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受欢迎的三角函数 >

3-6cos(x+pi/3)=0

解答

3 - 6 cos (x + \frac{π}{3}) = 0

解答

x = 2 πn, x = 2 πn + \frac{4 π}{3}

+1

度数

x = 0^{\circ} + 36 0^{\circ} n, x = 24 0^{\circ} + 36 0^{\circ} n

求解步骤

3 - 6 cos (x + \frac{π}{3}) = 0

将

3

到右边

3 - 6 cos (x + \frac{π}{3}) = 0

两边减去

3

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

化简

- 6 cos (x + \frac{π}{3}) = - 3

- 6 cos (x + \frac{π}{3}) = - 3

两边除以

- 6

- 6 cos (x + \frac{π}{3}) = - 3

两边除以

- 6

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

化简

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

化简

\frac{- 6 cos ( x + \frac{π}{3} )}{- 6} : cos (x + \frac{π}{3})

\frac{- 6 cos ( x + \frac{π}{3} )}{- 6}

使用分式法则:

\frac{- a}{- b} = \frac{a}{b}

= \frac{6 cos ( x + \frac{π}{3} )}{6}

数字相除:

\frac{6}{6} = 1

= cos (x + \frac{π}{3})

化简

\frac{- 3}{- 6} : \frac{1}{2}

\frac{- 3}{- 6}

使用分式法则:

\frac{- a}{- b} = \frac{a}{b}

= \frac{3}{6}

约分:

3

= \frac{1}{2}

cos (x + \frac{π}{3}) = \frac{1}{2}

cos (x + \frac{π}{3}) = \frac{1}{2}

cos (x + \frac{π}{3}) = \frac{1}{2}

cos (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}

x + \frac{π}{3} = \frac{π}{3} + 2 πn, x + \frac{π}{3} = \frac{5 π}{3} + 2 πn

x + \frac{π}{3} = \frac{π}{3} + 2 πn, x + \frac{π}{3} = \frac{5 π}{3} + 2 πn

解

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

x + \frac{π}{3} = \frac{π}{3} + 2 πn

两边减去

\frac{π}{3}

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

化简

x = 2 πn

解

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

x + \frac{π}{3} = \frac{5 π}{3} + 2 πn

将

\frac{π}{3}

到右边

x + \frac{π}{3} = \frac{5 π}{3} + 2 πn

两边减去

\frac{π}{3}

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

化简

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

化简

x + \frac{π}{3} - \frac{π}{3} : x

x + \frac{π}{3} - \frac{π}{3}

同类项相加:

\frac{π}{3} - \frac{π}{3} = 0

= x

化简

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

\frac{5 π}{3} + 2 πn - \frac{π}{3}

对同类项分组

= 2 πn - \frac{π}{3} + \frac{5 π}{3}

合并分式

- \frac{π}{3} + \frac{5 π}{3} : \frac{4 π}{3}

使用法则

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

= \frac{- π + 5 π}{3}

同类项相加:

- π + 5 π = 4 π

= \frac{4 π}{3}

= 2 πn + \frac{4 π}{3}

x = 2 πn + \frac{4 π}{3}

x = 2 πn + \frac{4 π}{3}

x = 2 πn + \frac{4 π}{3}

x = 2 πn, x = 2 πn + \frac{4 π}{3}

作图

流行的例子

sin (7.07 t) = 0.5

tan(x)= 1/(sqrt(3)),0<= x<2pi

tan (x) = \frac{1}{3}, 0 \leq x < 2 π

- 2 sin (2 x) = 2 π

arccos(θ)= 17/18

arccos (θ) = \frac{17}{18}

cos (θ) = - \frac{2}{9}