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شائع علم المثلثات >

sin(110-x/2)=-sin(70)

الحلّ

sin (11 0^{\circ} - \frac{x}{2}) = - sin (7 0^{\circ})

الحلّ

x = - 72 0^{\circ} n + 22 0^{\circ} - 2 (- 1.22173 \dots), x = - 36 0^{\circ} - 72 0^{\circ} n + 8 0^{\circ}

راديان

x = \frac{11 π}{9} - 2 (- 1.22173 \dots) - 4 πn, x = - 2 π + \frac{4 π}{9} - 4 πn

خطوات الحلّ

sin (11 0^{\circ} - \frac{x}{2}) = - sin (7 0^{\circ})

Apply trig inverse properties

sin (11 0^{\circ} - \frac{x}{2}) = - sin (7 0^{\circ})

sin (11 0^{\circ} - \frac{x}{2}) = - sin (7 0^{\circ}) :

حلول عامّة لـ

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

11 0^{\circ} - \frac{x}{2} = arcsin (- sin (7 0^{\circ})) + 36 0^{\circ} n, 11 0^{\circ} - \frac{x}{2} = 18 0^{\circ} + arcsin (sin (7 0^{\circ})) + 36 0^{\circ} n

11 0^{\circ} - \frac{x}{2} = arcsin (- sin (7 0^{\circ})) + 36 0^{\circ} n, 11 0^{\circ} - \frac{x}{2} = 18 0^{\circ} + arcsin (sin (7 0^{\circ})) + 36 0^{\circ} n

11 0^{\circ} - \frac{x}{2} = arcsin (- sin (7 0^{\circ})) + 36 0^{\circ} n

حلّ:

x = - 72 0^{\circ} n + 22 0^{\circ} - 2 arcsin (- sin (7 0^{\circ}))

11 0^{\circ} - \frac{x}{2} = arcsin (- sin (7 0^{\circ})) + 36 0^{\circ} n

انقل

11 0^{\circ}

إلى الجانب الأيمن

11 0^{\circ} - \frac{x}{2} = arcsin (- sin (7 0^{\circ})) + 36 0^{\circ} n

من الطرفين

11 0^{\circ}

اطرح

11 0^{\circ} - \frac{x}{2} - 11 0^{\circ} = arcsin (- sin (7 0^{\circ})) + 36 0^{\circ} n - 11 0^{\circ}

بسّط

- \frac{x}{2} = arcsin (- sin (7 0^{\circ})) + 36 0^{\circ} n - 11 0^{\circ}

- \frac{x}{2} = arcsin (- sin (7 0^{\circ})) + 36 0^{\circ} n - 11 0^{\circ}

2

اضرب الطرفين بـ

- \frac{x}{2} = arcsin (- sin (7 0^{\circ})) + 36 0^{\circ} n - 11 0^{\circ}

2

اضرب الطرفين بـ

2 (- \frac{x}{2}) = 2 arcsin (- sin (7 0^{\circ})) + 2 \cdot 36 0^{\circ} n - 2 \cdot 11 0^{\circ}

بسّط

2 (- \frac{x}{2}) = 2 arcsin (- sin (7 0^{\circ})) + 2 \cdot 36 0^{\circ} n - 2 \cdot 11 0^{\circ}

2 (- \frac{x}{2})

بسّط:

- x

2 (- \frac{x}{2})

(- a) = - a

:احذف الأقواس

= - 2 \cdot \frac{x}{2}

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

:اضرب كسور

= - \frac{x \cdot 2}{2}

2 :

إلغ العوامل المشتركة

= - x

2 arcsin (- sin (7 0^{\circ})) + 2 \cdot 36 0^{\circ} n - 2 \cdot 11 0^{\circ}

بسّط:

2 arcsin (- sin (7 0^{\circ})) + 72 0^{\circ} n - 22 0^{\circ}

2 arcsin (- sin (7 0^{\circ})) + 2 \cdot 36 0^{\circ} n - 2 \cdot 11 0^{\circ}

2 \cdot 36 0^{\circ} n = 72 0^{\circ} n

2 \cdot 36 0^{\circ} n

2 \cdot 2 = 4 :

اضرب الأعداد

= 72 0^{\circ} n

2 \cdot 11 0^{\circ} = 22 0^{\circ}

2 \cdot 11 0^{\circ}

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

:اضرب كسور

= 22 0^{\circ}

11 \cdot 2 = 22 :

اضرب الأعداد

= 22 0^{\circ}

2 :

إلغ العوامل المشتركة

= 22 0^{\circ}

= 2 arcsin (- sin (7 0^{\circ})) + 72 0^{\circ} n - 22 0^{\circ}

- x = 2 arcsin (- sin (7 0^{\circ})) + 72 0^{\circ} n - 22 0^{\circ}

- x = 2 arcsin (- sin (7 0^{\circ})) + 72 0^{\circ} n - 22 0^{\circ}

- x = 2 arcsin (- sin (7 0^{\circ})) + 72 0^{\circ} n - 22 0^{\circ}

- 1

اقسم الطرفين على

- x = 2 arcsin (- sin (7 0^{\circ})) + 72 0^{\circ} n - 22 0^{\circ}

- 1

اقسم الطرفين على

\frac{- x}{- 1} = \frac{2 arcsin ( - sin ( 7 0 ^{\circ} ) )}{- 1} + \frac{72 0 ^{\circ} n}{- 1} - \frac{22 0 ^{\circ}}{- 1}

بسّط

\frac{- x}{- 1} = \frac{2 arcsin ( - sin ( 7 0 ^{\circ} ) )}{- 1} + \frac{72 0 ^{\circ} n}{- 1} - \frac{22 0 ^{\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{2 arcsin ( - sin ( 7 0 ^{\circ} ) )}{- 1} + \frac{72 0 ^{\circ} n}{- 1} - \frac{22 0 ^{\circ}}{- 1}

بسّط:

- 72 0^{\circ} n + 22 0^{\circ} - 2 arcsin (- sin (7 0^{\circ}))

\frac{2 arcsin ( - sin ( 7 0 ^{\circ} ) )}{- 1} + \frac{72 0 ^{\circ} n}{- 1} - \frac{22 0 ^{\circ}}{- 1}

جمّع التعابير المتشابهة

= \frac{72 0 ^{\circ} n}{- 1} - \frac{22 0 ^{\circ}}{- 1} + \frac{2 arcsin ( - sin ( 7 0 ^{\circ} ) )}{- 1}

\frac{72 0 ^{\circ} n}{- 1} = - 72 0^{\circ} n

\frac{72 0 ^{\circ} n}{- 1}

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

: استخدم ميزات الكسور التالية

= - \frac{72 0 ^{\circ} n}{1}

\frac{a}{1} = a

فعّل القانون

= - 72 0^{\circ} n

= - 72 0^{\circ} n - \frac{22 0 ^{\circ}}{- 1} + \frac{2 arcsin ( - sin ( 7 0 ^{\circ} ) )}{- 1}

\frac{22 0 ^{\circ}}{- 1} = - 22 0^{\circ}

\frac{22 0 ^{\circ}}{- 1}

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

: استخدم ميزات الكسور التالية

= - \frac{22 0 ^{\circ}}{1}

\frac{a}{1} = a

: استخدم ميزات الكسور التالية

\frac{22 0 ^{\circ}}{1} = 22 0^{\circ}

= - 22 0^{\circ}

\frac{2 arcsin ( - sin ( 7 0 ^{\circ} ) )}{- 1} = - 2 arcsin (- sin (7 0^{\circ}))

\frac{2 arcsin ( - sin ( 7 0 ^{\circ} ) )}{- 1}

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

: استخدم ميزات الكسور التالية

= - \frac{2 arcsin ( - sin ( 7 0 ^{\circ} ) )}{1}

\frac{a}{1} = a

: استخدم ميزات الكسور التالية

\frac{2 arcsin ( - sin ( 7 0 ^{\circ} ) )}{1} = 2 arcsin (- sin (7 0^{\circ}))

= - 2 arcsin (- sin (7 0^{\circ}))

= - 72 0^{\circ} n - (- 22 0^{\circ}) - 2 arcsin (- sin (7 0^{\circ}))

- (- a) = a

فعّل القانون

= - 72 0^{\circ} n + 22 0^{\circ} - 2 arcsin (- sin (7 0^{\circ}))

x = - 72 0^{\circ} n + 22 0^{\circ} - 2 arcsin (- sin (7 0^{\circ}))

x = - 72 0^{\circ} n + 22 0^{\circ} - 2 arcsin (- sin (7 0^{\circ}))

x = - 72 0^{\circ} n + 22 0^{\circ} - 2 arcsin (- sin (7 0^{\circ}))

11 0^{\circ} - \frac{x}{2} = 18 0^{\circ} + arcsin (sin (7 0^{\circ})) + 36 0^{\circ} n

حلّ:

x = - 36 0^{\circ} - 72 0^{\circ} n + 8 0^{\circ}

11 0^{\circ} - \frac{x}{2} = 18 0^{\circ} + arcsin (sin (7 0^{\circ})) + 36 0^{\circ} n

arcsin (sin (7 0^{\circ})) = 7 0^{\circ}

arcsin (sin (7 0^{\circ}))

a rcs in (s in (x)) = x, - 9 0^{\circ} \leq x \leq 9 0^{\circ}

من أجل

- 9 0^{\circ} \leq 7 0^{\circ} \leq 9 0^{\circ}

= 7 0^{\circ}

11 0^{\circ} - \frac{x}{2} = 18 0^{\circ} + 7 0^{\circ} + 36 0^{\circ} n

انقل

11 0^{\circ}

إلى الجانب الأيمن

11 0^{\circ} - \frac{x}{2} = 18 0^{\circ} + 7 0^{\circ} + 36 0^{\circ} n

من الطرفين

11 0^{\circ}

اطرح

11 0^{\circ} - \frac{x}{2} - 11 0^{\circ} = 18 0^{\circ} + 7 0^{\circ} + 36 0^{\circ} n - 11 0^{\circ}

بسّط

11 0^{\circ} - \frac{x}{2} - 11 0^{\circ} = 18 0^{\circ} + 7 0^{\circ} + 36 0^{\circ} n - 11 0^{\circ}

11 0^{\circ} - \frac{x}{2} - 11 0^{\circ}

بسّط:

- \frac{x}{2}

11 0^{\circ} - \frac{x}{2} - 11 0^{\circ}

11 0^{\circ} - 11 0^{\circ} = 0 :

اجمع العناصر المتشابهة

= - \frac{x}{2}

18 0^{\circ} + 7 0^{\circ} + 36 0^{\circ} n - 11 0^{\circ}

بسّط:

18 0^{\circ} + 36 0^{\circ} n - 4 0^{\circ}

18 0^{\circ} + 7 0^{\circ} + 36 0^{\circ} n - 11 0^{\circ}

جمّع التعابير المتشابهة

= 18 0^{\circ} + 36 0^{\circ} n + 7 0^{\circ} - 11 0^{\circ}

7 0^{\circ} - 11 0^{\circ}

وحّد الكسور:

- 4 0^{\circ}

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

فعّل القانون

= \frac{126 0 ^{\circ} - 198 0 ^{\circ}}{18}

126 0^{\circ} - 198 0^{\circ} = - 72 0^{\circ} :

اجمع العناصر المتشابهة

= \frac{- 72 0 ^{\circ}}{18}

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

: استخدم ميزات الكسور التالية

= - 4 0^{\circ}

2 :

إلغ العوامل المشتركة

= - 4 0^{\circ}

= 18 0^{\circ} + 36 0^{\circ} n - 4 0^{\circ}

- \frac{x}{2} = 18 0^{\circ} + 36 0^{\circ} n - 4 0^{\circ}

- \frac{x}{2} = 18 0^{\circ} + 36 0^{\circ} n - 4 0^{\circ}

- \frac{x}{2} = 18 0^{\circ} + 36 0^{\circ} n - 4 0^{\circ}

2

اضرب الطرفين بـ

- \frac{x}{2} = 18 0^{\circ} + 36 0^{\circ} n - 4 0^{\circ}

2

اضرب الطرفين بـ

2 (- \frac{x}{2}) = 36 0^{\circ} + 2 \cdot 36 0^{\circ} n - 2 \cdot 4 0^{\circ}

بسّط

2 (- \frac{x}{2}) = 36 0^{\circ} + 2 \cdot 36 0^{\circ} n - 2 \cdot 4 0^{\circ}

2 (- \frac{x}{2})

بسّط:

- x

2 (- \frac{x}{2})

(- a) = - a

:احذف الأقواس

= - 2 \cdot \frac{x}{2}

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

:اضرب كسور

= - \frac{x \cdot 2}{2}

2 :

إلغ العوامل المشتركة

= - x

36 0^{\circ} + 2 \cdot 36 0^{\circ} n - 2 \cdot 4 0^{\circ}

بسّط:

36 0^{\circ} + 72 0^{\circ} n - 8 0^{\circ}

36 0^{\circ} + 2 \cdot 36 0^{\circ} n - 2 \cdot 4 0^{\circ}

2 \cdot 36 0^{\circ} n = 72 0^{\circ} n

2 \cdot 36 0^{\circ} n

2 \cdot 2 = 4 :

اضرب الأعداد

= 72 0^{\circ} n

2 \cdot 4 0^{\circ} = 8 0^{\circ}

2 \cdot 4 0^{\circ}

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

:اضرب كسور

= 8 0^{\circ}

2 \cdot 2 = 4 :

اضرب الأعداد

= 8 0^{\circ}

= 36 0^{\circ} + 72 0^{\circ} n - 8 0^{\circ}

- x = 36 0^{\circ} + 72 0^{\circ} n - 8 0^{\circ}

- x = 36 0^{\circ} + 72 0^{\circ} n - 8 0^{\circ}

- x = 36 0^{\circ} + 72 0^{\circ} n - 8 0^{\circ}

- 1

اقسم الطرفين على

- x = 36 0^{\circ} + 72 0^{\circ} n - 8 0^{\circ}

- 1

اقسم الطرفين على

\frac{- x}{- 1} = \frac{36 0 ^{\circ}}{- 1} + \frac{72 0 ^{\circ} n}{- 1} - \frac{8 0 ^{\circ}}{- 1}

بسّط

\frac{- x}{- 1} = \frac{36 0 ^{\circ}}{- 1} + \frac{72 0 ^{\circ} n}{- 1} - \frac{8 0 ^{\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{36 0 ^{\circ}}{- 1} + \frac{72 0 ^{\circ} n}{- 1} - \frac{8 0 ^{\circ}}{- 1}

بسّط:

- 36 0^{\circ} - 72 0^{\circ} n + 8 0^{\circ}

\frac{36 0 ^{\circ}}{- 1} + \frac{72 0 ^{\circ} n}{- 1} - \frac{8 0 ^{\circ}}{- 1}

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

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

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

: استخدم ميزات الكسور التالية

= - 36 0^{\circ}

\frac{a}{1} = a

فعّل القانون

= - 36 0^{\circ}

= - 36 0^{\circ} + \frac{72 0 ^{\circ} n}{- 1} - \frac{8 0 ^{\circ}}{- 1}

\frac{72 0 ^{\circ} n}{- 1} = - 72 0^{\circ} n

\frac{72 0 ^{\circ} n}{- 1}

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

: استخدم ميزات الكسور التالية

= - \frac{72 0 ^{\circ} n}{1}

\frac{a}{1} = a

فعّل القانون

= - 72 0^{\circ} n

= - 36 0^{\circ} - 72 0^{\circ} n - \frac{8 0 ^{\circ}}{- 1}

\frac{8 0 ^{\circ}}{- 1} = - 8 0^{\circ}

\frac{8 0 ^{\circ}}{- 1}

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

: استخدم ميزات الكسور التالية

= - \frac{8 0 ^{\circ}}{1}

\frac{a}{1} = a

: استخدم ميزات الكسور التالية

\frac{8 0 ^{\circ}}{1} = 8 0^{\circ}

= - 8 0^{\circ}

= - 36 0^{\circ} - 72 0^{\circ} n - (- 8 0^{\circ})

- (- a) = a

فعّل القانون

= - 36 0^{\circ} - 72 0^{\circ} n + 8 0^{\circ}

x = - 36 0^{\circ} - 72 0^{\circ} n + 8 0^{\circ}

x = - 36 0^{\circ} - 72 0^{\circ} n + 8 0^{\circ}

x = - 36 0^{\circ} - 72 0^{\circ} n + 8 0^{\circ}

x = - 72 0^{\circ} n + 22 0^{\circ} - 2 arcsin (- sin (7 0^{\circ})), x = - 36 0^{\circ} - 72 0^{\circ} n + 8 0^{\circ}

أظهر الحلّ بالتمثيل العشريّ

x = - 72 0^{\circ} n + 22 0^{\circ} - 2 (- 1.22173 \dots), x = - 36 0^{\circ} - 72 0^{\circ} n + 8 0^{\circ}

رسم

أمثلة شائعة

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(2 sin (x) - 1) (sin (x) + 0.5) = 0

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tan (θ) - 2 cos (θ) tan (θ) = 0

tan(x)=sec^2(x)-1

tan (x) = sec^{2} (x) - 1

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5 cos (x) = - 2 sin^{2} (x) + 4, 0 \leq x < 2 π

tan(x)=(4sqrt(3))/4

tan (x) = \frac{4 3}{4}