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受欢迎的三角函数 >

3cos(x)+9/2 =5+4cos(x)

解答

3 cos (x) + \frac{9}{2} = 5 + 4 cos (x)

解答

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

+1

度数

x = 12 0^{\circ} + 36 0^{\circ} n, x = 24 0^{\circ} + 36 0^{\circ} n

求解步骤

3 cos (x) + \frac{9}{2} = 5 + 4 cos (x)

用替代法求解

3 cos (x) + \frac{9}{2} = 5 + 4 cos (x)

令

: cos (x) = u

3 u + \frac{9}{2} = 5 + 4 u

3 u + \frac{9}{2} = 5 + 4 u : u = - \frac{1}{2}

3 u + \frac{9}{2} = 5 + 4 u

将

\frac{9}{2}

到右边

3 u + \frac{9}{2} = 5 + 4 u

两边减去

\frac{9}{2}

3 u + \frac{9}{2} - \frac{9}{2} = 5 + 4 u - \frac{9}{2}

化简

3 u + \frac{9}{2} - \frac{9}{2} = 5 + 4 u - \frac{9}{2}

化简

3 u + \frac{9}{2} - \frac{9}{2} : 3 u

3 u + \frac{9}{2} - \frac{9}{2}

同类项相加:

\frac{9}{2} - \frac{9}{2} = 0

= 3 u

化简

5 + 4 u - \frac{9}{2} : 4 u + \frac{1}{2}

5 + 4 u - \frac{9}{2}

合并分式

5 - \frac{9}{2} : \frac{1}{2}

5 - \frac{9}{2}

将项转换为分式:

5 = \frac{5 \cdot 2}{2}

= \frac{5 \cdot 2}{2} - \frac{9}{2}

因为分母相等，所以合并分式:

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

= \frac{5 \cdot 2 - 9}{2}

5 \cdot 2 - 9 = 1

5 \cdot 2 - 9

数字相乘:

5 \cdot 2 = 10

= 10 - 9

数字相减:

10 - 9 = 1

= 1

= \frac{1}{2}

= 4 u + \frac{1}{2}

3 u = 4 u + \frac{1}{2}

3 u = 4 u + \frac{1}{2}

3 u = 4 u + \frac{1}{2}

将

4 u

para o lado esquerdo

3 u = 4 u + \frac{1}{2}

两边减去

4 u

3 u - 4 u = 4 u + \frac{1}{2} - 4 u

化简

- u = \frac{1}{2}

- u = \frac{1}{2}

两边除以

- 1

- u = \frac{1}{2}

两边除以

- 1

\frac{- u}{- 1} = \frac{\frac{1}{2}}{- 1}

化简

\frac{- u}{- 1} = \frac{\frac{1}{2}}{- 1}

化简

\frac{- u}{- 1} : u

\frac{- u}{- 1}

使用分式法则:

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

= \frac{u}{1}

使用法则

\frac{a}{1} = a

= u

化简

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

\frac{\frac{1}{2}}{- 1}

使用分式法则:

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

= - \frac{\frac{1}{2}}{1}

使用分式法则:

\frac{a}{1} = a

\frac{\frac{1}{2}}{1} = \frac{1}{2}

= - \frac{1}{2}

u = - \frac{1}{2}

u = - \frac{1}{2}

u = - \frac{1}{2}

u = cos (x)

代回

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

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

cos (x) = - \frac{1}{2} : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

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

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

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

合并所有解

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

作图

流行的例子

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