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sin(pi/2-x)=-1,0<= x<= 360

الحلّ

sin (\frac{π}{2} - x) = - 1, 0^{\circ} \leq x \leq 36 0^{\circ}

الحلّ

x = 18 0^{\circ}

راديان

x = π

خطوات الحلّ

sin (\frac{π}{2} - x) = - 1, 0^{\circ} \leq x \leq 36 0^{\circ}

sin (9 0^{\circ} - x) = - 1 :

حلول عامّة لـ

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

9 0^{\circ} - x = 27 0^{\circ} + 36 0^{\circ} n

9 0^{\circ} - x = 27 0^{\circ} + 36 0^{\circ} n

9 0^{\circ} - x = 27 0^{\circ} + 36 0^{\circ} n

حلّ:

x = - 36 0^{\circ} n - 18 0^{\circ}

9 0^{\circ} - x = 27 0^{\circ} + 36 0^{\circ} n

انقل

9 0^{\circ}

إلى الجانب الأيمن

9 0^{\circ} - x = 27 0^{\circ} + 36 0^{\circ} n

من الطرفين

9 0^{\circ}

اطرح

9 0^{\circ} - x - 9 0^{\circ} = 27 0^{\circ} + 36 0^{\circ} n - 9 0^{\circ}

بسّط

9 0^{\circ} - x - 9 0^{\circ} = 27 0^{\circ} + 36 0^{\circ} n - 9 0^{\circ}

9 0^{\circ} - x - 9 0^{\circ}

بسّط:

- x

9 0^{\circ} - x - 9 0^{\circ}

9 0^{\circ} - 9 0^{\circ} = 0 :

اجمع العناصر المتشابهة

= - x

27 0^{\circ} + 36 0^{\circ} n - 9 0^{\circ}

بسّط:

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

27 0^{\circ} + 36 0^{\circ} n - 9 0^{\circ}

جمّع التعابير المتشابهة

= 36 0^{\circ} n - 9 0^{\circ} + 27 0^{\circ}

- 9 0^{\circ} + 27 0^{\circ}

وحّد الكسور:

18 0^{\circ}

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

فعّل القانون

= \frac{- 18 0 ^{\circ} + 54 0 ^{\circ}}{2}

- 18 0^{\circ} + 54 0^{\circ} = 36 0^{\circ} :

اجمع العناصر المتشابهة

= 18 0^{\circ}

\frac{2}{2} = 1 :

اقسم الأعداد

= 18 0^{\circ}

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

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

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

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

- 1

اقسم الطرفين على

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

- 1

اقسم الطرفين على

\frac{- x}{- 1} = \frac{36 0 ^{\circ} n}{- 1} + \frac{18 0 ^{\circ}}{- 1}

بسّط

\frac{- x}{- 1} = \frac{36 0 ^{\circ} n}{- 1} + \frac{18 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} n}{- 1} + \frac{18 0 ^{\circ}}{- 1}

بسّط:

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

\frac{36 0 ^{\circ} n}{- 1} + \frac{18 0 ^{\circ}}{- 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{18 0 ^{\circ}}{- 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}

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

x = - 36 0^{\circ} n - 18 0^{\circ}

x = - 36 0^{\circ} n - 18 0^{\circ}

x = - 36 0^{\circ} n - 18 0^{\circ}

x = - 36 0^{\circ} n - 18 0^{\circ}

0 \leq x \leq 36 0^{\circ} :

حلول للمدى

x = 18 0^{\circ}

أمثلة شائعة

2sin(5x)=-1

2 sin (5 x) = - 1

4sin^2(x)+8cos(x)-7=0

4 sin^{2} (x) + 8 cos (x) - 7 = 0

6(cos(b))^2+cos(b)-1=0

6 (cos (b))^{2} + cos (b) - 1 = 0

sin(θ)=(1.33)/(2.42)

sin (θ) = \frac{1.33}{2.42}

2tan(x)=3-tan^2(x),-2pi<= ,x<= pi

2 tan (x) = 3 - tan^{2} (x), - 2 π \leq, x \leq π