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شائع علم المثلثات >

15.8*sin(30x-90)+5=17

الحلّ

15.8 \cdot sin (30 x - 90) + 5 = 17

الحلّ

x = 3 + \frac{πn}{15} + \frac{0.86253 \dots}{30}, x = \frac{π}{30} + \frac{πn}{15} - \frac{0.86253 \dots}{30} + 3

درجات

x = 173.53465 \dots^{\circ} + 1 2^{\circ} n, x = 176.24001 \dots^{\circ} + 1 2^{\circ} n

خطوات الحلّ

15.8 sin (30 x - 90) + 5 = 17

10

اضرب الطرفين بـ

15.8 sin (30 x - 90) + 5 = 17

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

15.8 sin (30 x - 90) \cdot 10 + 5 \cdot 10 = 17 \cdot 10

بسّط

158 sin (30 x - 90) + 50 = 170

158 sin (30 x - 90) + 50 = 170

انقل

50

إلى الجانب الأيمن

158 sin (30 x - 90) + 50 = 170

من الطرفين

50

اطرح

158 sin (30 x - 90) + 50 - 50 = 170 - 50

بسّط

158 sin (30 x - 90) = 120

158 sin (30 x - 90) = 120

158

اقسم الطرفين على

158 sin (30 x - 90) = 120

158

اقسم الطرفين على

\frac{158 sin ( 30 x - 90 )}{158} = \frac{120}{158}

بسّط

sin (30 x - 90) = \frac{60}{79}

sin (30 x - 90) = \frac{60}{79}

Apply trig inverse properties

sin (30 x - 90) = \frac{60}{79}

sin (30 x - 90) = \frac{60}{79} :

حلول عامّة لـ

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

30 x - 90 = arcsin (\frac{60}{79}) + 2 πn, 30 x - 90 = π - arcsin (\frac{60}{79}) + 2 πn

30 x - 90 = arcsin (\frac{60}{79}) + 2 πn, 30 x - 90 = π - arcsin (\frac{60}{79}) + 2 πn

30 x - 90 = arcsin (\frac{60}{79}) + 2 πn

حلّ:

x = 3 + \frac{πn}{15} + \frac{arcsin ( \frac{60}{79} )}{30}

30 x - 90 = arcsin (\frac{60}{79}) + 2 πn

انقل

90

إلى الجانب الأيمن

30 x - 90 = arcsin (\frac{60}{79}) + 2 πn

للطرفين

90

أضف

30 x - 90 + 90 = arcsin (\frac{60}{79}) + 2 πn + 90

بسّط

30 x = arcsin (\frac{60}{79}) + 2 πn + 90

30 x = arcsin (\frac{60}{79}) + 2 πn + 90

30

اقسم الطرفين على

30 x = arcsin (\frac{60}{79}) + 2 πn + 90

30

اقسم الطرفين على

\frac{30 x}{30} = \frac{arcsin ( \frac{60}{79} )}{30} + \frac{2 πn}{30} + \frac{90}{30}

بسّط

\frac{30 x}{30} = \frac{arcsin ( \frac{60}{79} )}{30} + \frac{2 πn}{30} + \frac{90}{30}

\frac{30 x}{30}

بسّط:

x

\frac{30 x}{30}

\frac{30}{30} = 1 :

اقسم الأعداد

= x

\frac{arcsin ( \frac{60}{79} )}{30} + \frac{2 πn}{30} + \frac{90}{30}

بسّط:

3 + \frac{πn}{15} + \frac{arcsin ( \frac{60}{79} )}{30}

\frac{arcsin ( \frac{60}{79} )}{30} + \frac{2 πn}{30} + \frac{90}{30}

جمّع التعابير المتشابهة

= \frac{90}{30} + \frac{2 πn}{30} + \frac{arcsin ( \frac{60}{79} )}{30}

\frac{90}{30} = 3 :

اقسم الأعداد

= 3 + \frac{2 πn}{30} + \frac{arcsin ( \frac{60}{79} )}{30}

\frac{2 πn}{30}

اختزل:

\frac{πn}{15}

\frac{2 πn}{30}

2 :

إلغ العوامل المشتركة

= \frac{πn}{15}

= 3 + \frac{πn}{15} + \frac{arcsin ( \frac{60}{79} )}{30}

x = 3 + \frac{πn}{15} + \frac{arcsin ( \frac{60}{79} )}{30}

x = 3 + \frac{πn}{15} + \frac{arcsin ( \frac{60}{79} )}{30}

x = 3 + \frac{πn}{15} + \frac{arcsin ( \frac{60}{79} )}{30}

30 x - 90 = π - arcsin (\frac{60}{79}) + 2 πn

حلّ:

x = \frac{π}{30} + \frac{πn}{15} - \frac{arcsin ( \frac{60}{79} )}{30} + 3

30 x - 90 = π - arcsin (\frac{60}{79}) + 2 πn

انقل

90

إلى الجانب الأيمن

30 x - 90 = π - arcsin (\frac{60}{79}) + 2 πn

للطرفين

90

أضف

30 x - 90 + 90 = π - arcsin (\frac{60}{79}) + 2 πn + 90

بسّط

30 x = π - arcsin (\frac{60}{79}) + 2 πn + 90

30 x = π - arcsin (\frac{60}{79}) + 2 πn + 90

30

اقسم الطرفين على

30 x = π - arcsin (\frac{60}{79}) + 2 πn + 90

30

اقسم الطرفين على

\frac{30 x}{30} = \frac{π}{30} - \frac{arcsin ( \frac{60}{79} )}{30} + \frac{2 πn}{30} + \frac{90}{30}

بسّط

\frac{30 x}{30} = \frac{π}{30} - \frac{arcsin ( \frac{60}{79} )}{30} + \frac{2 πn}{30} + \frac{90}{30}

\frac{30 x}{30}

بسّط:

x

\frac{30 x}{30}

\frac{30}{30} = 1 :

اقسم الأعداد

= x

\frac{π}{30} - \frac{arcsin ( \frac{60}{79} )}{30} + \frac{2 πn}{30} + \frac{90}{30}

بسّط:

\frac{π}{30} + \frac{πn}{15} - \frac{arcsin ( \frac{60}{79} )}{30} + 3

\frac{π}{30} - \frac{arcsin ( \frac{60}{79} )}{30} + \frac{2 πn}{30} + \frac{90}{30}

جمّع التعابير المتشابهة

= \frac{π}{30} + \frac{90}{30} + \frac{2 πn}{30} - \frac{arcsin ( \frac{60}{79} )}{30}

\frac{90}{30} = 3 :

اقسم الأعداد

= \frac{π}{30} + 3 + \frac{2 πn}{30} - \frac{arcsin ( \frac{60}{79} )}{30}

\frac{2 πn}{30}

اختزل:

\frac{πn}{15}

\frac{2 πn}{30}

2 :

إلغ العوامل المشتركة

= \frac{πn}{15}

= \frac{π}{30} + 3 + \frac{πn}{15} - \frac{arcsin ( \frac{60}{79} )}{30}

جمّع التعابير المتشابهة

= \frac{π}{30} + \frac{πn}{15} - \frac{arcsin ( \frac{60}{79} )}{30} + 3

x = \frac{π}{30} + \frac{πn}{15} - \frac{arcsin ( \frac{60}{79} )}{30} + 3

x = \frac{π}{30} + \frac{πn}{15} - \frac{arcsin ( \frac{60}{79} )}{30} + 3

x = \frac{π}{30} + \frac{πn}{15} - \frac{arcsin ( \frac{60}{79} )}{30} + 3

x = 3 + \frac{πn}{15} + \frac{arcsin ( \frac{60}{79} )}{30}, x = \frac{π}{30} + \frac{πn}{15} - \frac{arcsin ( \frac{60}{79} )}{30} + 3

أظهر الحلّ بالتمثيل العشريّ

x = 3 + \frac{πn}{15} + \frac{0.86253 \dots}{30}, x = \frac{π}{30} + \frac{πn}{15} - \frac{0.86253 \dots}{30} + 3

رسم

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