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شائع علم المثلثات >

(368.02)/(sin(66-x))=(290)/(sin(38))

الحلّ

\frac{368.02}{sin ( 6 6 ^{\circ} - x )} = \frac{290}{sin ( 3 8 ^{\circ} )}

الحلّ

x = - 36 0^{\circ} n + 6 6^{\circ} - 0.89673 \dots, x = - 18 0^{\circ} - 36 0^{\circ} n + 6 6^{\circ} + 0.89673 \dots

راديان

x = \frac{11 π}{30} - 0.89673 \dots - 2 πn, x = - π + \frac{11 π}{30} + 0.89673 \dots - 2 πn

خطوات الحلّ

\frac{368.02}{sin ( 6 6 ^{\circ} - x )} = \frac{290}{sin ( 3 8 ^{\circ} )}

الضرب التقاطعي

\frac{368.02}{sin ( 6 6 ^{\circ} - x )} = \frac{290}{sin ( 3 8 ^{\circ} )}

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

الضرب التقاطعي

368.02 sin (3 8^{\circ}) = sin (6 6^{\circ} - x) \cdot 290

368.02 sin (3 8^{\circ}) = sin (6 6^{\circ} - x) \cdot 290

بدّل الأطراف

sin (6 6^{\circ} - x) \cdot 290 = 368.02 sin (3 8^{\circ})

290

اقسم الطرفين على

sin (6 6^{\circ} - x) \cdot 290 = 368.02 sin (3 8^{\circ})

290

اقسم الطرفين على

\frac{sin ( 6 6 ^{\circ} - x ) \cdot 290}{290} = \frac{368.02 sin ( 3 8 ^{\circ} )}{290}

بسّط

sin (6 6^{\circ} - x) = \frac{368.02 sin ( 3 8 ^{\circ} )}{290}

sin (6 6^{\circ} - x) = \frac{368.02 sin ( 3 8 ^{\circ} )}{290}

افحص الإجبات

جد نقاط غير معرّفة:

sin (6 6^{\circ} - x) = 0

وقم بمساواتها لصفر

\frac{368.02}{sin ( 6 6 ^{\circ} - x )}

خذ المقامات في

sin (6 6^{\circ} - x) = 0

النقاط التالية غير معرّفة

sin (6 6^{\circ} - x) = 0

ضمّ النقاط غير المعرّفة مع الحلول

sin (6 6^{\circ} - x) = \frac{368.02 sin ( 3 8 ^{\circ} )}{290}

Apply trig inverse properties

sin (6 6^{\circ} - x) = \frac{368.02 sin ( 3 8 ^{\circ} )}{290}

sin (6 6^{\circ} - x) = \frac{368.02 sin ( 3 8 ^{\circ} )}{290} :

حلول عامّة لـ

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

6 6^{\circ} - x = arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n, 6 6^{\circ} - x = 18 0^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n

6 6^{\circ} - x = arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n, 6 6^{\circ} - x = 18 0^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n

6 6^{\circ} - x = arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n

حلّ:

x = - 36 0^{\circ} n + 6 6^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

6 6^{\circ} - x = arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n

انقل

6 6^{\circ}

إلى الجانب الأيمن

6 6^{\circ} - x = arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n

من الطرفين

6 6^{\circ}

اطرح

6 6^{\circ} - x - 6 6^{\circ} = arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n - 6 6^{\circ}

بسّط

- x = arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n - 6 6^{\circ}

- x = arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n - 6 6^{\circ}

- 1

اقسم الطرفين على

- x = arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n - 6 6^{\circ}

- 1

اقسم الطرفين على

\frac{- x}{- 1} = \frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 6 ^{\circ}}{- 1}

بسّط

\frac{- x}{- 1} = \frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 6 ^{\circ}}{- 1}

\frac{- x}{- 1}

بسّط:

x

\frac{- x}{- 1}

\frac{- a}{- b} = \frac{a}{b}

: استخدم ميزات الكسور التالية

= \frac{x}{1}

\frac{a}{1} = a

فعّل القانون

= x

\frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 6 ^{\circ}}{- 1}

بسّط:

- 36 0^{\circ} n + 6 6^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

\frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 6 ^{\circ}}{- 1}

جمّع التعابير المتشابهة

= \frac{36 0 ^{\circ} n}{- 1} - \frac{6 6 ^{\circ}}{- 1} + \frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1}

\frac{36 0 ^{\circ} n}{- 1} = - 36 0^{\circ} n

\frac{36 0 ^{\circ} n}{- 1}

\frac{a}{- b} = - \frac{a}{b}

: استخدم ميزات الكسور التالية

= - \frac{36 0 ^{\circ} n}{1}

\frac{a}{1} = a

فعّل القانون

= - 36 0^{\circ} n

= - 36 0^{\circ} n - \frac{6 6 ^{\circ}}{- 1} + \frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1}

\frac{6 6 ^{\circ}}{- 1} = - 6 6^{\circ}

\frac{6 6 ^{\circ}}{- 1}

\frac{a}{- b} = - \frac{a}{b}

: استخدم ميزات الكسور التالية

= - \frac{6 6 ^{\circ}}{1}

\frac{a}{1} = a

: استخدم ميزات الكسور التالية

\frac{6 6 ^{\circ}}{1} = 6 6^{\circ}

= - 6 6^{\circ}

\frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1} = - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

\frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1}

\frac{a}{- b} = - \frac{a}{b}

: استخدم ميزات الكسور التالية

= - \frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{1}

\frac{a}{1} = a

: استخدم ميزات الكسور التالية

\frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{1} = arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

= - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

= - 36 0^{\circ} n - (- 6 6^{\circ}) - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

- (- a) = a

فعّل القانون

= - 36 0^{\circ} n + 6 6^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

x = - 36 0^{\circ} n + 6 6^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

x = - 36 0^{\circ} n + 6 6^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

x = - 36 0^{\circ} n + 6 6^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

6 6^{\circ} - x = 18 0^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n

حلّ:

x = - 18 0^{\circ} - 36 0^{\circ} n + 6 6^{\circ} + arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

6 6^{\circ} - x = 18 0^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n

انقل

6 6^{\circ}

إلى الجانب الأيمن

6 6^{\circ} - x = 18 0^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n

من الطرفين

6 6^{\circ}

اطرح

6 6^{\circ} - x - 6 6^{\circ} = 18 0^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n - 6 6^{\circ}

بسّط

- x = 18 0^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n - 6 6^{\circ}

- x = 18 0^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n - 6 6^{\circ}

- 1

اقسم الطرفين على

- x = 18 0^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}) + 36 0^{\circ} n - 6 6^{\circ}

- 1

اقسم الطرفين على

\frac{- x}{- 1} = \frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 6 ^{\circ}}{- 1}

بسّط

\frac{- x}{- 1} = \frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 6 ^{\circ}}{- 1}

\frac{- x}{- 1}

بسّط:

x

\frac{- x}{- 1}

\frac{- a}{- b} = \frac{a}{b}

: استخدم ميزات الكسور التالية

= \frac{x}{1}

\frac{a}{1} = a

فعّل القانون

= x

\frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 6 ^{\circ}}{- 1}

بسّط:

- 18 0^{\circ} - 36 0^{\circ} n + 6 6^{\circ} + arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

\frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 6 ^{\circ}}{- 1}

جمّع التعابير المتشابهة

= \frac{18 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 6 ^{\circ}}{- 1} - \frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1}

\frac{18 0 ^{\circ}}{- 1} = - 18 0^{\circ}

\frac{18 0 ^{\circ}}{- 1}

\frac{a}{- b} = - \frac{a}{b}

: استخدم ميزات الكسور التالية

= - 18 0^{\circ}

\frac{a}{1} = a

فعّل القانون

= - 18 0^{\circ}

= - 18 0^{\circ} + \frac{36 0 ^{\circ} n}{- 1} - \frac{6 6 ^{\circ}}{- 1} - \frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1}

\frac{36 0 ^{\circ} n}{- 1} = - 36 0^{\circ} n

\frac{36 0 ^{\circ} n}{- 1}

\frac{a}{- b} = - \frac{a}{b}

: استخدم ميزات الكسور التالية

= - \frac{36 0 ^{\circ} n}{1}

\frac{a}{1} = a

فعّل القانون

= - 36 0^{\circ} n

= - 18 0^{\circ} - 36 0^{\circ} n - \frac{6 6 ^{\circ}}{- 1} - \frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1}

\frac{6 6 ^{\circ}}{- 1} = - 6 6^{\circ}

\frac{6 6 ^{\circ}}{- 1}

\frac{a}{- b} = - \frac{a}{b}

: استخدم ميزات الكسور التالية

= - \frac{6 6 ^{\circ}}{1}

\frac{a}{1} = a

: استخدم ميزات الكسور التالية

\frac{6 6 ^{\circ}}{1} = 6 6^{\circ}

= - 6 6^{\circ}

\frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1} = - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

\frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{- 1}

\frac{a}{- b} = - \frac{a}{b}

: استخدم ميزات الكسور التالية

= - \frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{1}

\frac{a}{1} = a

: استخدم ميزات الكسور التالية

\frac{arcsin ( \frac{368.02 s i n ( 3 8 ^{\circ} )}{290} )}{1} = arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

= - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

= - 18 0^{\circ} - 36 0^{\circ} n - (- 6 6^{\circ}) - (- arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}))

- (- a) = a

فعّل القانون

= - 18 0^{\circ} - 36 0^{\circ} n + 6 6^{\circ} + arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

x = - 18 0^{\circ} - 36 0^{\circ} n + 6 6^{\circ} + arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

x = - 18 0^{\circ} - 36 0^{\circ} n + 6 6^{\circ} + arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

x = - 18 0^{\circ} - 36 0^{\circ} n + 6 6^{\circ} + arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

x = - 36 0^{\circ} n + 6 6^{\circ} - arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290}), x = - 18 0^{\circ} - 36 0^{\circ} n + 6 6^{\circ} + arcsin (\frac{368.02 sin ( 3 8 ^{\circ} )}{290})

أظهر الحلّ بالتمثيل العشريّ

x = - 36 0^{\circ} n + 6 6^{\circ} - 0.89673 \dots, x = - 18 0^{\circ} - 36 0^{\circ} n + 6 6^{\circ} + 0.89673 \dots

رسم

أمثلة شائعة

cos^2(x)sec(x)=1

cos^{2} (x) sec (x) = 1

tan(x)=(9.3)/(7.5)

tan (x) = \frac{9.3}{7.5}

sin(α)+cos(α)=1

sin (α) + cos (α) = 1

2sin(θ)=sqrt(3)tan(θ)

2 sin (θ) = 3 tan (θ)

sin(θ)=-0.78

sin (θ) = - 0.78