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شائع علم المثلثات >

sin(5x-1)= 4/5

الحلّ

sin (5 x - 1) = \frac{4}{5}

الحلّ

x = \frac{0.92729 \dots}{5} + \frac{2 πn}{5} + \frac{1}{5}, x = \frac{π}{5} - \frac{0.92729 \dots}{5} + \frac{2 πn}{5} + \frac{1}{5}

+1

درجات

x = 22.08517 \dots^{\circ} + 7 2^{\circ} n, x = 36.83313 \dots^{\circ} + 7 2^{\circ} n

خطوات الحلّ

sin (5 x - 1) = \frac{4}{5}

Apply trig inverse properties

sin (5 x - 1) = \frac{4}{5}

sin (5 x - 1) = \frac{4}{5} :

حلول عامّة لـ

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

5 x - 1 = arcsin (\frac{4}{5}) + 2 πn, 5 x - 1 = π - arcsin (\frac{4}{5}) + 2 πn

5 x - 1 = arcsin (\frac{4}{5}) + 2 πn, 5 x - 1 = π - arcsin (\frac{4}{5}) + 2 πn

5 x - 1 = arcsin (\frac{4}{5}) + 2 πn

حلّ:

x = \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

5 x - 1 = arcsin (\frac{4}{5}) + 2 πn

انقل

1

إلى الجانب الأيمن

5 x - 1 = arcsin (\frac{4}{5}) + 2 πn

للطرفين

1

أضف

5 x - 1 + 1 = arcsin (\frac{4}{5}) + 2 πn + 1

بسّط

5 x = arcsin (\frac{4}{5}) + 2 πn + 1

5 x = arcsin (\frac{4}{5}) + 2 πn + 1

5

اقسم الطرفين على

5 x = arcsin (\frac{4}{5}) + 2 πn + 1

5

اقسم الطرفين على

\frac{5 x}{5} = \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

بسّط

x = \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

x = \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

5 x - 1 = π - arcsin (\frac{4}{5}) + 2 πn

حلّ:

x = \frac{π}{5} - \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

5 x - 1 = π - arcsin (\frac{4}{5}) + 2 πn

انقل

1

إلى الجانب الأيمن

5 x - 1 = π - arcsin (\frac{4}{5}) + 2 πn

للطرفين

1

أضف

5 x - 1 + 1 = π - arcsin (\frac{4}{5}) + 2 πn + 1

بسّط

5 x = π - arcsin (\frac{4}{5}) + 2 πn + 1

5 x = π - arcsin (\frac{4}{5}) + 2 πn + 1

5

اقسم الطرفين على

5 x = π - arcsin (\frac{4}{5}) + 2 πn + 1

5

اقسم الطرفين على

\frac{5 x}{5} = \frac{π}{5} - \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

بسّط

x = \frac{π}{5} - \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

x = \frac{π}{5} - \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

x = \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}, x = \frac{π}{5} - \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

أظهر الحلّ بالتمثيل العشريّ

x = \frac{0.92729 \dots}{5} + \frac{2 πn}{5} + \frac{1}{5}, x = \frac{π}{5} - \frac{0.92729 \dots}{5} + \frac{2 πn}{5} + \frac{1}{5}

رسم

أمثلة شائعة

sin^4(x)+cos^2(x)=2

5tan(x)=15cot(x)

solvefor x,arctan(x)=arctan(y)