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شائع علم المثلثات >

cos(0.568x-2.595)=0

الحلّ

cos (0.568 x - 2.595) = 0

الحلّ

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

درجات

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

خطوات الحلّ

cos (0.568 x - 2.595) = 0

cos (0.568 x - 2.595) = 0 :

حلول عامّة لـ

cos (x)

periodicity table with

2 πn

cycle:

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

0.568 x - 2.595 = \frac{π}{2} + 2 πn

حلّ:

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

0.568 x - 2.595 = \frac{π}{2} + 2 πn

1000

اضرب الطرفين بـ

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

بسّط

568 x - 2595 = 500 π + 2000 πn

568 x - 2595 = 500 π + 2000 πn

انقل

2595

إلى الجانب الأيمن

568 x - 2595 = 500 π + 2000 πn

للطرفين

2595

أضف

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

بسّط

568 x = 500 π + 2000 πn + 2595

568 x = 500 π + 2000 πn + 2595

568

اقسم الطرفين على

568 x = 500 π + 2000 πn + 2595

568

اقسم الطرفين على

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

بسّط

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

\frac{568 x}{568}

بسّط:

x

\frac{568 x}{568}

\frac{568}{568} = 1 :

اقسم الأعداد

= x

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

بسّط:

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

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

جمّع التعابير المتشابهة

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

\frac{500 π}{568}

اختزل:

\frac{125 π}{142}

\frac{500 π}{568}

4 :

إلغ العوامل المشتركة

= \frac{125 π}{142}

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

\frac{2000 πn}{568}

اختزل:

\frac{250 πn}{71}

\frac{2000 πn}{568}

8 :

إلغ العوامل المشتركة

= \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}

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

حلّ:

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

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

1000

اضرب الطرفين بـ

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

بسّط

568 x - 2595 = 1500 π + 2000 πn

568 x - 2595 = 1500 π + 2000 πn

انقل

2595

إلى الجانب الأيمن

568 x - 2595 = 1500 π + 2000 πn

للطرفين

2595

أضف

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

بسّط

568 x = 1500 π + 2000 πn + 2595

568 x = 1500 π + 2000 πn + 2595

568

اقسم الطرفين على

568 x = 1500 π + 2000 πn + 2595

568

اقسم الطرفين على

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

بسّط

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

\frac{568 x}{568}

بسّط:

x

\frac{568 x}{568}

\frac{568}{568} = 1 :

اقسم الأعداد

= x

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

بسّط:

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

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

جمّع التعابير المتشابهة

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

\frac{1500 π}{568}

اختزل:

\frac{375 π}{142}

\frac{1500 π}{568}

4 :

إلغ العوامل المشتركة

= \frac{375 π}{142}

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

\frac{2000 πn}{568}

اختزل:

\frac{250 πn}{71}

\frac{2000 πn}{568}

8 :

إلغ العوامل المشتركة

= \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}

رسم

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