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شائع علم المثلثات >

20=2.891sin(0.016d-1.183)+18.512

الحلّ

20 = 2.891 sin (0.016 d - 1.183) + 18.512

الحلّ

d = \frac{0.54065 \dots}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}, d = \frac{π}{0.016} - \frac{0.54065 \dots}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

درجات

d = 6172.39781 \dots^{\circ} + 2250 0^{\circ} n, d = 13550.21558 \dots^{\circ} + 2250 0^{\circ} n

خطوات الحلّ

20 = 2.891 sin (0.016 d - 1.183) + 18.512

بدّل الأطراف

2.891 sin (0.016 d - 1.183) + 18.512 = 20

1000

اضرب الطرفين بـ

2.891 sin (0.016 d - 1.183) + 18.512 = 20

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

2.891 sin (0.016 d - 1.183) \cdot 1000 + 18.512 \cdot 1000 = 20 \cdot 1000

بسّط

2891 sin (0.016 d - 1.183) + 18512 = 20000

2891 sin (0.016 d - 1.183) + 18512 = 20000

انقل

18512

إلى الجانب الأيمن

2891 sin (0.016 d - 1.183) + 18512 = 20000

من الطرفين

18512

اطرح

2891 sin (0.016 d - 1.183) + 18512 - 18512 = 20000 - 18512

بسّط

2891 sin (0.016 d - 1.183) = 1488

2891 sin (0.016 d - 1.183) = 1488

2891

اقسم الطرفين على

2891 sin (0.016 d - 1.183) = 1488

2891

اقسم الطرفين على

\frac{2891 sin ( 0.016 d - 1.183 )}{2891} = \frac{1488}{2891}

بسّط

sin (0.016 d - 1.183) = \frac{1488}{2891}

sin (0.016 d - 1.183) = \frac{1488}{2891}

Apply trig inverse properties

sin (0.016 d - 1.183) = \frac{1488}{2891}

sin (0.016 d - 1.183) = \frac{1488}{2891} :

حلول عامّة لـ

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

0.016 d - 1.183 = arcsin (\frac{1488}{2891}) + 2 πn, 0.016 d - 1.183 = π - arcsin (\frac{1488}{2891}) + 2 πn

0.016 d - 1.183 = arcsin (\frac{1488}{2891}) + 2 πn, 0.016 d - 1.183 = π - arcsin (\frac{1488}{2891}) + 2 πn

0.016 d - 1.183 = arcsin (\frac{1488}{2891}) + 2 πn

حلّ:

d = \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

0.016 d - 1.183 = arcsin (\frac{1488}{2891}) + 2 πn

انقل

1.183

إلى الجانب الأيمن

0.016 d - 1.183 = arcsin (\frac{1488}{2891}) + 2 πn

للطرفين

1.183

أضف

0.016 d - 1.183 + 1.183 = arcsin (\frac{1488}{2891}) + 2 πn + 1.183

بسّط

0.016 d = arcsin (\frac{1488}{2891}) + 2 πn + 1.183

0.016 d = arcsin (\frac{1488}{2891}) + 2 πn + 1.183

0.016

اقسم الطرفين على

0.016 d = arcsin (\frac{1488}{2891}) + 2 πn + 1.183

0.016

اقسم الطرفين على

\frac{0.016 d}{0.016} = \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

بسّط

d = \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

d = \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

0.016 d - 1.183 = π - arcsin (\frac{1488}{2891}) + 2 πn

حلّ:

d = \frac{π}{0.016} - \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

0.016 d - 1.183 = π - arcsin (\frac{1488}{2891}) + 2 πn

انقل

1.183

إلى الجانب الأيمن

0.016 d - 1.183 = π - arcsin (\frac{1488}{2891}) + 2 πn

للطرفين

1.183

أضف

0.016 d - 1.183 + 1.183 = π - arcsin (\frac{1488}{2891}) + 2 πn + 1.183

بسّط

0.016 d = π - arcsin (\frac{1488}{2891}) + 2 πn + 1.183

0.016 d = π - arcsin (\frac{1488}{2891}) + 2 πn + 1.183

0.016

اقسم الطرفين على

0.016 d = π - arcsin (\frac{1488}{2891}) + 2 πn + 1.183

0.016

اقسم الطرفين على

\frac{0.016 d}{0.016} = \frac{π}{0.016} - \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

بسّط

d = \frac{π}{0.016} - \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

d = \frac{π}{0.016} - \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

d = \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}, d = \frac{π}{0.016} - \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

أظهر الحلّ بالتمثيل العشريّ

d = \frac{0.54065 \dots}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}, d = \frac{π}{0.016} - \frac{0.54065 \dots}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

رسم

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