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受欢迎的三角函数 >

solvefor x,T(7)=3.15cos(pi/6 x)+19.15

解答

求解

x, T (7) = 3.15 cos (\frac{π}{6} x) + 19.15

解答

x = \frac{6 arccos ( \frac{140 T - 383}{63} )}{π} + 12 n, x = - \frac{6 arccos ( \frac{140 T - 383}{63} )}{π} + 12 n

求解步骤

T (7) = 3.15 cos (\frac{π}{6} x) + 19.15

交换两边

3.15 cos (\frac{π}{6} x) + 19.15 = T \cdot 7

在两边乘以

100

3.15 cos (\frac{π}{6} x) + 19.15 = T \cdot 7

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

3.15 cos (\frac{π}{6} x) \cdot 100 + 19.15 \cdot 100 = T \cdot 7 \cdot 100

整理后得

315 cos (\frac{π}{6} x) + 1915 = 700 T

315 cos (\frac{π}{6} x) + 1915 = 700 T

将

1915

到右边

315 cos (\frac{π}{6} x) + 1915 = 700 T

两边减去

1915

315 cos (\frac{π}{6} x) + 1915 - 1915 = 700 T - 1915

化简

315 cos (\frac{π}{6} x) = 700 T - 1915

315 cos (\frac{π}{6} x) = 700 T - 1915

两边除以

315

315 cos (\frac{π}{6} x) = 700 T - 1915

两边除以

315

\frac{315 cos ( \frac{π}{6} x )}{315} = \frac{700 T}{315} - \frac{1915}{315}

化简

\frac{315 cos ( \frac{π}{6} x )}{315} = \frac{700 T}{315} - \frac{1915}{315}

化简

\frac{315 cos ( \frac{π}{6} x )}{315} : cos (\frac{π}{6} x)

\frac{315 cos ( \frac{π}{6} x )}{315}

数字相除:

\frac{315}{315} = 1

= cos (\frac{π}{6} x)

化简

\frac{700 T}{315} - \frac{1915}{315} : \frac{140 T - 383}{63}

\frac{700 T}{315} - \frac{1915}{315}

使用法则

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

= \frac{700 T - 1915}{315}

分解

700 T - 1915 : 5 (140 T - 383)

700 T - 1915

改写为

= 5 \cdot 140 T - 5 \cdot 383

因式分解出通项

5

= 5 (140 T - 383)

= \frac{5 ( 140 T - 383 )}{315}

约分:

5

= \frac{140 T - 383}{63}

cos (\frac{π}{6} x) = \frac{140 T - 383}{63}

cos (\frac{π}{6} x) = \frac{140 T - 383}{63}

cos (\frac{π}{6} x) = \frac{140 T - 383}{63}

使用反三角函数性质

cos (\frac{π}{6} x) = \frac{140 T - 383}{63}

cos (\frac{π}{6} x) = \frac{140 T - 383}{63}

的通解

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

\frac{π}{6} x = arccos (\frac{140 T - 383}{63}) + 2 πn, \frac{π}{6} x = - arccos (\frac{140 T - 383}{63}) + 2 πn

\frac{π}{6} x = arccos (\frac{140 T - 383}{63}) + 2 πn, \frac{π}{6} x = - arccos (\frac{140 T - 383}{63}) + 2 πn

解

\frac{π}{6} x = arccos (\frac{140 T - 383}{63}) + 2 πn : x = \frac{6 arccos ( \frac{140 T - 383}{63} )}{π} + 12 n

\frac{π}{6} x = arccos (\frac{140 T - 383}{63}) + 2 πn

在两边乘以

6

\frac{π}{6} x = arccos (\frac{140 T - 383}{63}) + 2 πn

在两边乘以

6

6 \cdot \frac{π}{6} x = 6 arccos (\frac{140 T - 383}{63}) + 6 \cdot 2 πn

化简

6 \cdot \frac{π}{6} x = 6 arccos (\frac{140 T - 383}{63}) + 6 \cdot 2 πn

化简

6 \cdot \frac{π}{6} x : π x

6 \cdot \frac{π}{6} x

分式相乘:

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

= \frac{6 π}{6} x

约分:

6

= x π

化简

6 arccos (\frac{140 T - 383}{63}) + 6 \cdot 2 πn : 6 arccos (\frac{140 T - 383}{63}) + 12 πn

6 arccos (\frac{140 T - 383}{63}) + 6 \cdot 2 πn

数字相乘:

6 \cdot 2 = 12

= 6 arccos (\frac{140 T - 383}{63}) + 12 πn

π x = 6 arccos (\frac{140 T - 383}{63}) + 12 πn

π x = 6 arccos (\frac{140 T - 383}{63}) + 12 πn

π x = 6 arccos (\frac{140 T - 383}{63}) + 12 πn

两边除以

π

π x = 6 arccos (\frac{140 T - 383}{63}) + 12 πn

两边除以

π

\frac{π x}{π} = \frac{6 arccos ( \frac{140 T - 383}{63} )}{π} + \frac{12 πn}{π}

化简

x = \frac{6 arccos ( \frac{140 T - 383}{63} )}{π} + 12 n

x = \frac{6 arccos ( \frac{140 T - 383}{63} )}{π} + 12 n

解

\frac{π}{6} x = - arccos (\frac{140 T - 383}{63}) + 2 πn : x = - \frac{6 arccos ( \frac{140 T - 383}{63} )}{π} + 12 n

\frac{π}{6} x = - arccos (\frac{140 T - 383}{63}) + 2 πn

在两边乘以

6

\frac{π}{6} x = - arccos (\frac{140 T - 383}{63}) + 2 πn

在两边乘以

6

6 \cdot \frac{π}{6} x = - 6 arccos (\frac{140 T - 383}{63}) + 6 \cdot 2 πn

化简

6 \cdot \frac{π}{6} x = - 6 arccos (\frac{140 T - 383}{63}) + 6 \cdot 2 πn

化简

6 \cdot \frac{π}{6} x : π x

6 \cdot \frac{π}{6} x

分式相乘:

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

= \frac{6 π}{6} x

约分:

6

= x π

化简

- 6 arccos (\frac{140 T - 383}{63}) + 6 \cdot 2 πn : - 6 arccos (\frac{140 T - 383}{63}) + 12 πn

- 6 arccos (\frac{140 T - 383}{63}) + 6 \cdot 2 πn

数字相乘:

6 \cdot 2 = 12

= - 6 arccos (\frac{140 T - 383}{63}) + 12 πn

π x = - 6 arccos (\frac{140 T - 383}{63}) + 12 πn

π x = - 6 arccos (\frac{140 T - 383}{63}) + 12 πn

π x = - 6 arccos (\frac{140 T - 383}{63}) + 12 πn

两边除以

π

π x = - 6 arccos (\frac{140 T - 383}{63}) + 12 πn

两边除以

π

\frac{π x}{π} = - \frac{6 arccos ( \frac{140 T - 383}{63} )}{π} + \frac{12 πn}{π}

化简

x = - \frac{6 arccos ( \frac{140 T - 383}{63} )}{π} + 12 n

x = - \frac{6 arccos ( \frac{140 T - 383}{63} )}{π} + 12 n

x = \frac{6 arccos ( \frac{140 T - 383}{63} )}{π} + 12 n, x = - \frac{6 arccos ( \frac{140 T - 383}{63} )}{π} + 12 n

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