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شائع علم المثلثات >

8sin((3.14)/(4*x))=7

الحلّ

8 sin (\frac{3.14}{4 \cdot x}) = 7

الحلّ

x = \frac{3.14}{4 ( 1.06543 \dots + 2 πn )}, x = \frac{3.14}{4 ( π - 1.06543 \dots + 2 πn )}

+1

درجات

x = 0^{\circ} + 6.12049 \dots^{\circ} n, x = 0^{\circ} + 5.38046 \dots^{\circ} n

خطوات الحلّ

8 sin (\frac{3.14}{4 x}) = 7

8

اقسم الطرفين على

8 sin (\frac{3.14}{4 x}) = 7

8

اقسم الطرفين على

\frac{8 sin ( \frac{3.14}{4 x} )}{8} = \frac{7}{8}

بسّط

sin (\frac{3.14}{4 x}) = \frac{7}{8}

sin (\frac{3.14}{4 x}) = \frac{7}{8}

Apply trig inverse properties

sin (\frac{3.14}{4 x}) = \frac{7}{8}

sin (\frac{3.14}{4 x}) = \frac{7}{8} :

حلول عامّة لـ

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

\frac{3.14}{4 x} = arcsin (\frac{7}{8}) + 2 πn, \frac{3.14}{4 x} = π - arcsin (\frac{7}{8}) + 2 πn

\frac{3.14}{4 x} = arcsin (\frac{7}{8}) + 2 πn, \frac{3.14}{4 x} = π - arcsin (\frac{7}{8}) + 2 πn

\frac{3.14}{4 x} = arcsin (\frac{7}{8}) + 2 πn

حلّ:

x = \frac{3.14}{4 ( arcsin ( \frac{7}{8} ) + 2 πn )}; n \neq = - \frac{arcsin ( \frac{7}{8} )}{2 π}

\frac{3.14}{4 x} = arcsin (\frac{7}{8}) + 2 πn

x

اضرب الطرفين بـ

\frac{3.14}{4 x} = arcsin (\frac{7}{8}) + 2 πn

x

اضرب الطرفين بـ

\frac{3.14}{4 x} x = arcsin (\frac{7}{8}) x + 2 πn x

بسّط

\frac{3.14}{4} = arcsin (\frac{7}{8}) x + 2 πn x

\frac{3.14}{4} = arcsin (\frac{7}{8}) x + 2 πn x

بدّل الأطراف

arcsin (\frac{7}{8}) x + 2 πn x = \frac{3.14}{4}

arcsin (\frac{7}{8}) x + 2 πn x

حلل إلى عوامل:

x (arcsin (\frac{7}{8}) + 2 πn)

arcsin (\frac{7}{8}) x + 2 πn x

x

قم باخراج العامل المشترك

= x (arcsin (\frac{7}{8}) + 2 πn)

x (arcsin (\frac{7}{8}) + 2 πn) = \frac{3.14}{4}

arcsin (\frac{7}{8}) + 2 πn; n \neq = - \frac{arcsin ( \frac{7}{8} )}{2 π}

اقسم الطرفين على

x (arcsin (\frac{7}{8}) + 2 πn) = \frac{3.14}{4}

arcsin (\frac{7}{8}) + 2 πn; n \neq = - \frac{arcsin ( \frac{7}{8} )}{2 π}

اقسم الطرفين على

\frac{x ( arcsin ( \frac{7}{8} ) + 2 πn )}{arcsin ( \frac{7}{8} ) + 2 πn} = \frac{\frac{3.14}{4}}{arcsin ( \frac{7}{8} ) + 2 πn}; n \neq = - \frac{arcsin ( \frac{7}{8} )}{2 π}

بسّط

\frac{x ( arcsin ( \frac{7}{8} ) + 2 πn )}{arcsin ( \frac{7}{8} ) + 2 πn} = \frac{\frac{3.14}{4}}{arcsin ( \frac{7}{8} ) + 2 πn}

\frac{x ( arcsin ( \frac{7}{8} ) + 2 πn )}{arcsin ( \frac{7}{8} ) + 2 πn}

بسّط:

x

\frac{x ( arcsin ( \frac{7}{8} ) + 2 πn )}{arcsin ( \frac{7}{8} ) + 2 πn}

arcsin (\frac{7}{8}) + 2 πn :

إلغ العوامل المشتركة

= x

\frac{\frac{3.14}{4}}{arcsin ( \frac{7}{8} ) + 2 πn}

بسّط:

\frac{3.14}{4 ( arcsin ( \frac{7}{8} ) + 2 πn )}

\frac{\frac{3.14}{4}}{arcsin ( \frac{7}{8} ) + 2 πn}

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

: استخدم ميزات الكسور التالية

= \frac{3.14}{4 ( arcsin ( \frac{7}{8} ) + 2 πn )}

x = \frac{3.14}{4 ( arcsin ( \frac{7}{8} ) + 2 πn )}; n \neq = - \frac{arcsin ( \frac{7}{8} )}{2 π}

x = \frac{3.14}{4 ( arcsin ( \frac{7}{8} ) + 2 πn )}; n \neq = - \frac{arcsin ( \frac{7}{8} )}{2 π}

x = \frac{3.14}{4 ( arcsin ( \frac{7}{8} ) + 2 πn )}; n \neq = - \frac{arcsin ( \frac{7}{8} )}{2 π}

\frac{3.14}{4 x} = π - arcsin (\frac{7}{8}) + 2 πn

حلّ:

x = \frac{3.14}{4 ( π - arcsin ( \frac{7}{8} ) + 2 πn )}; n \neq = \frac{- π + arcsin ( \frac{7}{8} )}{2 π}

\frac{3.14}{4 x} = π - arcsin (\frac{7}{8}) + 2 πn

x

اضرب الطرفين بـ

\frac{3.14}{4 x} = π - arcsin (\frac{7}{8}) + 2 πn

x

اضرب الطرفين بـ

\frac{3.14}{4 x} x = π x - arcsin (\frac{7}{8}) x + 2 πn x

بسّط

\frac{3.14}{4} = π x - arcsin (\frac{7}{8}) x + 2 πn x

\frac{3.14}{4} = π x - arcsin (\frac{7}{8}) x + 2 πn x

بدّل الأطراف

π x - arcsin (\frac{7}{8}) x + 2 πn x = \frac{3.14}{4}

π x - arcsin (\frac{7}{8}) x + 2 πn x

حلل إلى عوامل:

x (π - arcsin (\frac{7}{8}) + 2 πn)

π x - arcsin (\frac{7}{8}) x + 2 πn x

x

قم باخراج العامل المشترك

= x (π - arcsin (\frac{7}{8}) + 2 πn)

x (π - arcsin (\frac{7}{8}) + 2 πn) = \frac{3.14}{4}

π - arcsin (\frac{7}{8}) + 2 πn; n \neq = \frac{- π + arcsin ( \frac{7}{8} )}{2 π}

اقسم الطرفين على

x (π - arcsin (\frac{7}{8}) + 2 πn) = \frac{3.14}{4}

π - arcsin (\frac{7}{8}) + 2 πn; n \neq = \frac{- π + arcsin ( \frac{7}{8} )}{2 π}

اقسم الطرفين على

\frac{x ( π - arcsin ( \frac{7}{8} ) + 2 πn )}{π - arcsin ( \frac{7}{8} ) + 2 πn} = \frac{\frac{3.14}{4}}{π - arcsin ( \frac{7}{8} ) + 2 πn}; n \neq = \frac{- π + arcsin ( \frac{7}{8} )}{2 π}

بسّط

\frac{x ( π - arcsin ( \frac{7}{8} ) + 2 πn )}{π - arcsin ( \frac{7}{8} ) + 2 πn} = \frac{\frac{3.14}{4}}{π - arcsin ( \frac{7}{8} ) + 2 πn}

\frac{x ( π - arcsin ( \frac{7}{8} ) + 2 πn )}{π - arcsin ( \frac{7}{8} ) + 2 πn}

بسّط:

x

\frac{x ( π - arcsin ( \frac{7}{8} ) + 2 πn )}{π - arcsin ( \frac{7}{8} ) + 2 πn}

π - arcsin (\frac{7}{8}) + 2 πn :

إلغ العوامل المشتركة

= x

\frac{\frac{3.14}{4}}{π - arcsin ( \frac{7}{8} ) + 2 πn}

بسّط:

\frac{3.14}{4 ( π - arcsin ( \frac{7}{8} ) + 2 πn )}

\frac{\frac{3.14}{4}}{π - arcsin ( \frac{7}{8} ) + 2 πn}

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

: استخدم ميزات الكسور التالية

= \frac{3.14}{4 ( π - arcsin ( \frac{7}{8} ) + 2 πn )}

x = \frac{3.14}{4 ( π - arcsin ( \frac{7}{8} ) + 2 πn )}; n \neq = \frac{- π + arcsin ( \frac{7}{8} )}{2 π}

x = \frac{3.14}{4 ( π - arcsin ( \frac{7}{8} ) + 2 πn )}; n \neq = \frac{- π + arcsin ( \frac{7}{8} )}{2 π}

x = \frac{3.14}{4 ( π - arcsin ( \frac{7}{8} ) + 2 πn )}; n \neq = \frac{- π + arcsin ( \frac{7}{8} )}{2 π}

x = \frac{3.14}{4 ( arcsin ( \frac{7}{8} ) + 2 πn )}, x = \frac{3.14}{4 ( π - arcsin ( \frac{7}{8} ) + 2 πn )}

أظهر الحلّ بالتمثيل العشريّ

x = \frac{3.14}{4 ( 1.06543 \dots + 2 πn )}, x = \frac{3.14}{4 ( π - 1.06543 \dots + 2 πn )}

رسم

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