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受欢迎的三角函数 >

4.797896cos(0.568x-2.595)=0

解答

4.797896 cos (0.568 x - 2.595) = 0

解答

x = \frac{125 π}{142} + \frac{2595}{568} + \frac{250 πn}{71}, x = \frac{2595}{568} + \frac{375 π}{142} + \frac{250 πn}{71}

度数

x = 420.21575 \dots^{\circ} + 633.80281 \dots^{\circ} n, x = 737.11716 \dots^{\circ} + 633.80281 \dots^{\circ} n

求解步骤

4.797896 cos (0.568 x - 2.595) = 0

两边除以

4.797896

4.797896 cos (0.568 x - 2.595) = 0

两边除以

4.797896

\frac{4.797896 cos ( 0.568 x - 2.595 )}{4.797896} = \frac{0}{4.797896}

化简

cos (0.568 x - 2.595) = 0

cos (0.568 x - 2.595) = 0

cos (0.568 x - 2.595) = 0

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}

0.568 x - 2.595 = \frac{π}{2} + 2 πn, 0.568 x - 2.595 = \frac{3 π}{2} + 2 πn

0.568 x - 2.595 = \frac{π}{2} + 2 πn, 0.568 x - 2.595 = \frac{3 π}{2} + 2 πn

解

0.568 x - 2.595 = \frac{π}{2} + 2 πn : x = \frac{125 π}{142} + \frac{2595}{568} + \frac{250 πn}{71}

0.568 x - 2.595 = \frac{π}{2} + 2 πn

在两边乘以

1000

0.568 x - 2.595 = \frac{π}{2} + 2 πn

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

3

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

1000

0.568 x \cdot 1000 - 2.595 \cdot 1000 = \frac{π}{2} \cdot 1000 + 2 πn \cdot 1000

整理后得

568 x - 2595 = 500 π + 2000 πn

568 x - 2595 = 500 π + 2000 πn

将

2595

到右边

568 x - 2595 = 500 π + 2000 πn

两边加上

2595

568 x - 2595 + 2595 = 500 π + 2000 πn + 2595

化简

568 x = 500 π + 2000 πn + 2595

568 x = 500 π + 2000 πn + 2595

两边除以

568

568 x = 500 π + 2000 πn + 2595

两边除以

568

\frac{568 x}{568} = \frac{500 π}{568} + \frac{2000 πn}{568} + \frac{2595}{568}

化简

\frac{568 x}{568} = \frac{500 π}{568} + \frac{2000 πn}{568} + \frac{2595}{568}

化简

\frac{568 x}{568} : x

\frac{568 x}{568}

数字相除:

\frac{568}{568} = 1

= x

化简

\frac{500 π}{568} + \frac{2000 πn}{568} + \frac{2595}{568} : \frac{125 π}{142} + \frac{2595}{568} + \frac{250 πn}{71}

\frac{500 π}{568} + \frac{2000 πn}{568} + \frac{2595}{568}

对同类项分组

= \frac{500 π}{568} + \frac{2595}{568} + \frac{2000 πn}{568}

消掉

\frac{500 π}{568} : \frac{125 π}{142}

\frac{500 π}{568}

约分:

4

= \frac{125 π}{142}

= \frac{125 π}{142} + \frac{2595}{568} + \frac{2000 πn}{568}

消掉

\frac{2000 πn}{568} : \frac{250 πn}{71}

\frac{2000 πn}{568}

约分:

8

= \frac{250 πn}{71}

= \frac{125 π}{142} + \frac{2595}{568} + \frac{250 πn}{71}

x = \frac{125 π}{142} + \frac{2595}{568} + \frac{250 πn}{71}

x = \frac{125 π}{142} + \frac{2595}{568} + \frac{250 πn}{71}

x = \frac{125 π}{142} + \frac{2595}{568} + \frac{250 πn}{71}

解

0.568 x - 2.595 = \frac{3 π}{2} + 2 πn : x = \frac{2595}{568} + \frac{375 π}{142} + \frac{250 πn}{71}

0.568 x - 2.595 = \frac{3 π}{2} + 2 πn

在两边乘以

1000

0.568 x - 2.595 = \frac{3 π}{2} + 2 πn

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

3

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

1000

0.568 x \cdot 1000 - 2.595 \cdot 1000 = \frac{3 π}{2} \cdot 1000 + 2 πn \cdot 1000

整理后得

568 x - 2595 = 1500 π + 2000 πn

568 x - 2595 = 1500 π + 2000 πn

将

2595

到右边

568 x - 2595 = 1500 π + 2000 πn

两边加上

2595

568 x - 2595 + 2595 = 1500 π + 2000 πn + 2595

化简

568 x = 1500 π + 2000 πn + 2595

568 x = 1500 π + 2000 πn + 2595

两边除以

568

568 x = 1500 π + 2000 πn + 2595

两边除以

568

\frac{568 x}{568} = \frac{1500 π}{568} + \frac{2000 πn}{568} + \frac{2595}{568}

化简

\frac{568 x}{568} = \frac{1500 π}{568} + \frac{2000 πn}{568} + \frac{2595}{568}

化简

\frac{568 x}{568} : x

\frac{568 x}{568}

数字相除:

\frac{568}{568} = 1

= x

化简

\frac{1500 π}{568} + \frac{2000 πn}{568} + \frac{2595}{568} : \frac{2595}{568} + \frac{375 π}{142} + \frac{250 πn}{71}

\frac{1500 π}{568} + \frac{2000 πn}{568} + \frac{2595}{568}

对同类项分组

= \frac{2595}{568} + \frac{1500 π}{568} + \frac{2000 πn}{568}

消掉

\frac{1500 π}{568} : \frac{375 π}{142}

\frac{1500 π}{568}

约分:

4

= \frac{375 π}{142}

= \frac{2595}{568} + \frac{375 π}{142} + \frac{2000 πn}{568}

消掉

\frac{2000 πn}{568} : \frac{250 πn}{71}

\frac{2000 πn}{568}

约分:

8

= \frac{250 πn}{71}

= \frac{2595}{568} + \frac{375 π}{142} + \frac{250 πn}{71}

x = \frac{2595}{568} + \frac{375 π}{142} + \frac{250 πn}{71}

x = \frac{2595}{568} + \frac{375 π}{142} + \frac{250 πn}{71}

x = \frac{2595}{568} + \frac{375 π}{142} + \frac{250 πn}{71}

x = \frac{125 π}{142} + \frac{2595}{568} + \frac{250 πn}{71}, x = \frac{2595}{568} + \frac{375 π}{142} + \frac{250 πn}{71}

作图

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