zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

1.5=2.75cos(30(x-4))+3.25

解答

1.5 = 2.75 cos (30 (x - 4)) + 3.25

解答

x = \frac{2.26057 \dots}{30} + \frac{πn}{15} + 4, x = - \frac{2.26057 \dots}{30} + \frac{πn}{15} + 4

+1

度数

x = 233.50049 \dots^{\circ} + 1 2^{\circ} n, x = 224.86574 \dots^{\circ} + 1 2^{\circ} n

求解步骤

1.5 = 2.75 cos (30 (x - 4)) + 3.25

交换两边

2.75 cos (30 (x - 4)) + 3.25 = 1.5

在两边乘以

100

2.75 cos (30 (x - 4)) + 3.25 = 1.5

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

2.75 cos (30 (x - 4)) \cdot 100 + 3.25 \cdot 100 = 1.5 \cdot 100

整理后得

275 cos (30 (x - 4)) + 325 = 150

275 cos (30 (x - 4)) + 325 = 150

将

325

到右边

275 cos (30 (x - 4)) + 325 = 150

两边减去

325

275 cos (30 (x - 4)) + 325 - 325 = 150 - 325

化简

275 cos (30 (x - 4)) = - 175

275 cos (30 (x - 4)) = - 175

两边除以

275

275 cos (30 (x - 4)) = - 175

两边除以

275

\frac{275 cos ( 30 ( x - 4 ) )}{275} = \frac{- 175}{275}

化简

\frac{275 cos ( 30 ( x - 4 ) )}{275} = \frac{- 175}{275}

化简

\frac{275 cos ( 30 ( x - 4 ) )}{275} : cos (30 (x - 4))

\frac{275 cos ( 30 ( x - 4 ) )}{275}

数字相除:

\frac{275}{275} = 1

= cos (30 (x - 4))

化简

\frac{- 175}{275} : - \frac{7}{11}

\frac{- 175}{275}

使用分式法则:

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

= - \frac{175}{275}

约分:

25

= - \frac{7}{11}

cos (30 (x - 4)) = - \frac{7}{11}

cos (30 (x - 4)) = - \frac{7}{11}

cos (30 (x - 4)) = - \frac{7}{11}

使用反三角函数性质

cos (30 (x - 4)) = - \frac{7}{11}

cos (30 (x - 4)) = - \frac{7}{11}

的通解

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

30 (x - 4) = arccos (- \frac{7}{11}) + 2 πn, 30 (x - 4) = - arccos (- \frac{7}{11}) + 2 πn

30 (x - 4) = arccos (- \frac{7}{11}) + 2 πn, 30 (x - 4) = - arccos (- \frac{7}{11}) + 2 πn

解

30 (x - 4) = arccos (- \frac{7}{11}) + 2 πn : x = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

30 (x - 4) = arccos (- \frac{7}{11}) + 2 πn

两边除以

30

30 (x - 4) = arccos (- \frac{7}{11}) + 2 πn

两边除以

30

\frac{30 ( x - 4 )}{30} = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{2 πn}{30}

化简

x - 4 = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15}

x - 4 = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15}

将

4

到右边

x - 4 = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15}

两边加上

4

x - 4 + 4 = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

化简

x = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

x = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

解

30 (x - 4) = - arccos (- \frac{7}{11}) + 2 πn : x = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

30 (x - 4) = - arccos (- \frac{7}{11}) + 2 πn

两边除以

30

30 (x - 4) = - arccos (- \frac{7}{11}) + 2 πn

两边除以

30

\frac{30 ( x - 4 )}{30} = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{2 πn}{30}

化简

x - 4 = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15}

x - 4 = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15}

将

4

到右边

x - 4 = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15}

两边加上

4

x - 4 + 4 = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

化简

x = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

x = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

x = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4, x = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

以小数形式表示解

x = \frac{2.26057 \dots}{30} + \frac{πn}{15} + 4, x = - \frac{2.26057 \dots}{30} + \frac{πn}{15} + 4

作图

流行的例子

sin (x) = (\frac{5}{12})

sin (x) = \frac{97}{270}

sqrt(3)cos(3x)+1=0

3 cos (3 x) + 1 = 0

sin (2 A) = sin (A)

csc (θ) = \frac{3}{2}