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شائع علم المثلثات >

cos(1/(3x))= 1/3

الحلّ

cos (\frac{1}{3 x}) = \frac{1}{3}

الحلّ

x = \frac{1}{3 ( 1.23095 \dots + 2 πn )}, x = \frac{1}{3 ( 2 π - 1.23095 \dots + 2 πn )}

+1

درجات

x = 0^{\circ} + 2.54168 \dots^{\circ} n, x = 0^{\circ} + 1.68486 \dots^{\circ} n

خطوات الحلّ

cos (\frac{1}{3 x}) = \frac{1}{3}

Apply trig inverse properties

cos (\frac{1}{3 x}) = \frac{1}{3}

cos (\frac{1}{3 x}) = \frac{1}{3} :

حلول عامّة لـ

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

\frac{1}{3 x} = arccos (\frac{1}{3}) + 2 πn, \frac{1}{3 x} = 2 π - arccos (\frac{1}{3}) + 2 πn

\frac{1}{3 x} = arccos (\frac{1}{3}) + 2 πn, \frac{1}{3 x} = 2 π - arccos (\frac{1}{3}) + 2 πn

\frac{1}{3 x} = arccos (\frac{1}{3}) + 2 πn

حلّ:

x = \frac{1}{3 ( arccos ( \frac{1}{3} ) + 2 πn )}; n \neq = - \frac{arccos ( \frac{1}{3} )}{2 π}

\frac{1}{3 x} = arccos (\frac{1}{3}) + 2 πn

x

اضرب الطرفين بـ

\frac{1}{3 x} = arccos (\frac{1}{3}) + 2 πn

x

اضرب الطرفين بـ

\frac{1}{3 x} x = arccos (\frac{1}{3}) x + 2 πn x

بسّط

\frac{1}{3} = arccos (\frac{1}{3}) x + 2 πn x

\frac{1}{3} = arccos (\frac{1}{3}) x + 2 πn x

بدّل الأطراف

arccos (\frac{1}{3}) x + 2 πn x = \frac{1}{3}

arccos (\frac{1}{3}) x + 2 πn x

حلل إلى عوامل:

x (arccos (\frac{1}{3}) + 2 πn)

arccos (\frac{1}{3}) x + 2 πn x

x

قم باخراج العامل المشترك

= x (arccos (\frac{1}{3}) + 2 πn)

x (arccos (\frac{1}{3}) + 2 πn) = \frac{1}{3}

arccos (\frac{1}{3}) + 2 πn; n \neq = - \frac{arccos ( \frac{1}{3} )}{2 π}

اقسم الطرفين على

x (arccos (\frac{1}{3}) + 2 πn) = \frac{1}{3}

arccos (\frac{1}{3}) + 2 πn; n \neq = - \frac{arccos ( \frac{1}{3} )}{2 π}

اقسم الطرفين على

\frac{x ( arccos ( \frac{1}{3} ) + 2 πn )}{arccos ( \frac{1}{3} ) + 2 πn} = \frac{\frac{1}{3}}{arccos ( \frac{1}{3} ) + 2 πn}; n \neq = - \frac{arccos ( \frac{1}{3} )}{2 π}

بسّط

\frac{x ( arccos ( \frac{1}{3} ) + 2 πn )}{arccos ( \frac{1}{3} ) + 2 πn} = \frac{\frac{1}{3}}{arccos ( \frac{1}{3} ) + 2 πn}

\frac{x ( arccos ( \frac{1}{3} ) + 2 πn )}{arccos ( \frac{1}{3} ) + 2 πn}

بسّط:

x

\frac{x ( arccos ( \frac{1}{3} ) + 2 πn )}{arccos ( \frac{1}{3} ) + 2 πn}

arccos (\frac{1}{3}) + 2 πn :

إلغ العوامل المشتركة

= x

\frac{\frac{1}{3}}{arccos ( \frac{1}{3} ) + 2 πn}

بسّط:

\frac{1}{3 ( arccos ( \frac{1}{3} ) + 2 πn )}

\frac{\frac{1}{3}}{arccos ( \frac{1}{3} ) + 2 πn}

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

: استخدم ميزات الكسور التالية

= \frac{1}{3 ( arccos ( \frac{1}{3} ) + 2 πn )}

x = \frac{1}{3 ( arccos ( \frac{1}{3} ) + 2 πn )}; n \neq = - \frac{arccos ( \frac{1}{3} )}{2 π}

x = \frac{1}{3 ( arccos ( \frac{1}{3} ) + 2 πn )}; n \neq = - \frac{arccos ( \frac{1}{3} )}{2 π}

x = \frac{1}{3 ( arccos ( \frac{1}{3} ) + 2 πn )}; n \neq = - \frac{arccos ( \frac{1}{3} )}{2 π}

\frac{1}{3 x} = 2 π - arccos (\frac{1}{3}) + 2 πn

حلّ:

x = \frac{1}{3 ( 2 π - arccos ( \frac{1}{3} ) + 2 πn )}; n \neq = \frac{- 2 π + arccos ( \frac{1}{3} )}{2 π}

\frac{1}{3 x} = 2 π - arccos (\frac{1}{3}) + 2 πn

x

اضرب الطرفين بـ

\frac{1}{3 x} = 2 π - arccos (\frac{1}{3}) + 2 πn

x

اضرب الطرفين بـ

\frac{1}{3 x} x = 2 π x - arccos (\frac{1}{3}) x + 2 πn x

بسّط

\frac{1}{3} = 2 π x - arccos (\frac{1}{3}) x + 2 πn x

\frac{1}{3} = 2 π x - arccos (\frac{1}{3}) x + 2 πn x

بدّل الأطراف

2 π x - arccos (\frac{1}{3}) x + 2 πn x = \frac{1}{3}

2 π x - arccos (\frac{1}{3}) x + 2 πn x

حلل إلى عوامل:

x (2 π - arccos (\frac{1}{3}) + 2 πn)

2 π x - arccos (\frac{1}{3}) x + 2 πn x

x

قم باخراج العامل المشترك

= x (2 π - arccos (\frac{1}{3}) + 2 πn)

x (2 π - arccos (\frac{1}{3}) + 2 πn) = \frac{1}{3}

2 π - arccos (\frac{1}{3}) + 2 πn; n \neq = \frac{- 2 π + arccos ( \frac{1}{3} )}{2 π}

اقسم الطرفين على

x (2 π - arccos (\frac{1}{3}) + 2 πn) = \frac{1}{3}

2 π - arccos (\frac{1}{3}) + 2 πn; n \neq = \frac{- 2 π + arccos ( \frac{1}{3} )}{2 π}

اقسم الطرفين على

\frac{x ( 2 π - arccos ( \frac{1}{3} ) + 2 πn )}{2 π - arccos ( \frac{1}{3} ) + 2 πn} = \frac{\frac{1}{3}}{2 π - arccos ( \frac{1}{3} ) + 2 πn}; n \neq = \frac{- 2 π + arccos ( \frac{1}{3} )}{2 π}

بسّط

\frac{x ( 2 π - arccos ( \frac{1}{3} ) + 2 πn )}{2 π - arccos ( \frac{1}{3} ) + 2 πn} = \frac{\frac{1}{3}}{2 π - arccos ( \frac{1}{3} ) + 2 πn}

\frac{x ( 2 π - arccos ( \frac{1}{3} ) + 2 πn )}{2 π - arccos ( \frac{1}{3} ) + 2 πn}

بسّط:

x

\frac{x ( 2 π - arccos ( \frac{1}{3} ) + 2 πn )}{2 π - arccos ( \frac{1}{3} ) + 2 πn}

2 π - arccos (\frac{1}{3}) + 2 πn :

إلغ العوامل المشتركة

= x

\frac{\frac{1}{3}}{2 π - arccos ( \frac{1}{3} ) + 2 πn}

بسّط:

\frac{1}{3 ( 2 π - arccos ( \frac{1}{3} ) + 2 πn )}

\frac{\frac{1}{3}}{2 π - arccos ( \frac{1}{3} ) + 2 πn}

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

: استخدم ميزات الكسور التالية

= \frac{1}{3 ( 2 π - arccos ( \frac{1}{3} ) + 2 πn )}

x = \frac{1}{3 ( 2 π - arccos ( \frac{1}{3} ) + 2 πn )}; n \neq = \frac{- 2 π + arccos ( \frac{1}{3} )}{2 π}

x = \frac{1}{3 ( 2 π - arccos ( \frac{1}{3} ) + 2 πn )}; n \neq = \frac{- 2 π + arccos ( \frac{1}{3} )}{2 π}

x = \frac{1}{3 ( 2 π - arccos ( \frac{1}{3} ) + 2 πn )}; n \neq = \frac{- 2 π + arccos ( \frac{1}{3} )}{2 π}

x = \frac{1}{3 ( arccos ( \frac{1}{3} ) + 2 πn )}, x = \frac{1}{3 ( 2 π - arccos ( \frac{1}{3} ) + 2 πn )}

أظهر الحلّ بالتمثيل العشريّ

x = \frac{1}{3 ( 1.23095 \dots + 2 πn )}, x = \frac{1}{3 ( 2 π - 1.23095 \dots + 2 πn )}

رسم

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