English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

شائع علم المثلثات >

4sin^2(x-60)=3

الحلّ

4 sin^{2} (x - 6 0^{\circ}) = 3

الحلّ

x = 12 0^{\circ} + 36 0^{\circ} n, x = 36 0^{\circ} n + 18 0^{\circ}, x = 36 0^{\circ} n + 30 0^{\circ}, x = 36 0^{\circ} n + 36 0^{\circ}

راديان

x = \frac{2 π}{3} + 2 πn, x = π + 2 πn, x = \frac{5 π}{3} + 2 πn, x = 2 π + 2 πn

خطوات الحلّ

4 sin^{2} (x - 6 0^{\circ}) = 3

بالاستعانة بطريقة التعويض

4 sin^{2} (x - 6 0^{\circ}) = 3

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

على افتراض أنّ

4 u^{2} = 3

4 u^{2} = 3 : u = \frac{3}{2}, u = - \frac{3}{2}

4 u^{2} = 3

4

اقسم الطرفين على

4 u^{2} = 3

4

اقسم الطرفين على

\frac{4 u ^{2}}{4} = \frac{3}{4}

بسّط

u^{2} = \frac{3}{4}

u^{2} = \frac{3}{4}

x = f (a), - f (a)

الحلول هي

x^{2} = f (a)

لـ

u = \frac{3}{4}, u = - \frac{3}{4}

\frac{3}{4} = \frac{3}{2}

\frac{3}{4}

a \geq 0, b \geq 0

بافتراض أنّ

n \frac{a}{b} = \frac{n a}{n b}

:فعّل قانون الجذور

= \frac{3}{4}

4 = 2

4

4 = 2^{2} :

حلّل العدد لعوامله أوّليّة

= 2^{2}

n a^{n} = a

:فعْل قانون الجذور

2^{2} = 2

= 2

= \frac{3}{2}

- \frac{3}{4} = - \frac{3}{2}

- \frac{3}{4}

\frac{3}{4}

بسّط:

\frac{3}{2}

\frac{3}{4}

a \geq 0, b \geq 0

بافتراض أنّ

n \frac{a}{b} = \frac{n a}{n b}

:فعّل قانون الجذور

= \frac{3}{4}

4 = 2

4

4 = 2^{2} :

حلّل العدد لعوامله أوّليّة

= 2^{2}

n a^{n} = a

:فعْل قانون الجذور

2^{2} = 2

= 2

= \frac{3}{2}

= - \frac{3}{2}

u = \frac{3}{2}, u = - \frac{3}{2}

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

استبدل مجددًا

sin (x - 6 0^{\circ}) = \frac{3}{2}, sin (x - 6 0^{\circ}) = - \frac{3}{2}

sin (x - 6 0^{\circ}) = \frac{3}{2}, sin (x - 6 0^{\circ}) = - \frac{3}{2}

sin (x - 6 0^{\circ}) = \frac{3}{2} : x = 12 0^{\circ} + 36 0^{\circ} n, x = 36 0^{\circ} n + 18 0^{\circ}

sin (x - 6 0^{\circ}) = \frac{3}{2}

sin (x - 6 0^{\circ}) = \frac{3}{2} :

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}

x - 6 0^{\circ} = 6 0^{\circ} + 36 0^{\circ} n, x - 6 0^{\circ} = 12 0^{\circ} + 36 0^{\circ} n

x - 6 0^{\circ} = 6 0^{\circ} + 36 0^{\circ} n, x - 6 0^{\circ} = 12 0^{\circ} + 36 0^{\circ} n

x - 6 0^{\circ} = 6 0^{\circ} + 36 0^{\circ} n

حلّ:

x = 12 0^{\circ} + 36 0^{\circ} n

x - 6 0^{\circ} = 6 0^{\circ} + 36 0^{\circ} n

انقل

6 0^{\circ}

إلى الجانب الأيمن

x - 6 0^{\circ} = 6 0^{\circ} + 36 0^{\circ} n

للطرفين

6 0^{\circ}

أضف

x - 6 0^{\circ} + 6 0^{\circ} = 6 0^{\circ} + 36 0^{\circ} n + 6 0^{\circ}

بسّط

x - 6 0^{\circ} + 6 0^{\circ} = 6 0^{\circ} + 36 0^{\circ} n + 6 0^{\circ}

x - 6 0^{\circ} + 6 0^{\circ}

بسّط:

x

x - 6 0^{\circ} + 6 0^{\circ}

- 6 0^{\circ} + 6 0^{\circ} = 0 :

اجمع العناصر المتشابهة

= x

6 0^{\circ} + 36 0^{\circ} n + 6 0^{\circ}

بسّط:

12 0^{\circ} + 36 0^{\circ} n

6 0^{\circ} + 36 0^{\circ} n + 6 0^{\circ}

جمّع التعابير المتشابهة

= 6 0^{\circ} + 6 0^{\circ} + 36 0^{\circ} n

6 0^{\circ} + 6 0^{\circ}

وحّد الكسور:

12 0^{\circ}

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

فعّل القانون

= \frac{18 0 ^{\circ} + 18 0 ^{\circ}}{3}

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

اجمع العناصر المتشابهة

= 12 0^{\circ}

= 12 0^{\circ} + 36 0^{\circ} n

x = 12 0^{\circ} + 36 0^{\circ} n

x = 12 0^{\circ} + 36 0^{\circ} n

x = 12 0^{\circ} + 36 0^{\circ} n

x - 6 0^{\circ} = 12 0^{\circ} + 36 0^{\circ} n

حلّ:

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

x - 6 0^{\circ} = 12 0^{\circ} + 36 0^{\circ} n

انقل

6 0^{\circ}

إلى الجانب الأيمن

x - 6 0^{\circ} = 12 0^{\circ} + 36 0^{\circ} n

للطرفين

6 0^{\circ}

أضف

x - 6 0^{\circ} + 6 0^{\circ} = 12 0^{\circ} + 36 0^{\circ} n + 6 0^{\circ}

بسّط

x - 6 0^{\circ} + 6 0^{\circ} = 12 0^{\circ} + 36 0^{\circ} n + 6 0^{\circ}

x - 6 0^{\circ} + 6 0^{\circ}

بسّط:

x

x - 6 0^{\circ} + 6 0^{\circ}

- 6 0^{\circ} + 6 0^{\circ} = 0 :

اجمع العناصر المتشابهة

= x

12 0^{\circ} + 36 0^{\circ} n + 6 0^{\circ}

بسّط:

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

12 0^{\circ} + 36 0^{\circ} n + 6 0^{\circ}

جمّع التعابير المتشابهة

= 36 0^{\circ} n + 6 0^{\circ} + 12 0^{\circ}

6 0^{\circ} + 12 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} + 36 0 ^{\circ}}{3}

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

اجمع العناصر المتشابهة

= 18 0^{\circ}

\frac{3}{3} = 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}

x = 12 0^{\circ} + 36 0^{\circ} n, x = 36 0^{\circ} n + 18 0^{\circ}

sin (x - 6 0^{\circ}) = - \frac{3}{2} : x = 36 0^{\circ} n + 30 0^{\circ}, x = 36 0^{\circ} n + 36 0^{\circ}

sin (x - 6 0^{\circ}) = - \frac{3}{2}

sin (x - 6 0^{\circ}) = - \frac{3}{2} :

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}

x - 6 0^{\circ} = 24 0^{\circ} + 36 0^{\circ} n, x - 6 0^{\circ} = 30 0^{\circ} + 36 0^{\circ} n

x - 6 0^{\circ} = 24 0^{\circ} + 36 0^{\circ} n, x - 6 0^{\circ} = 30 0^{\circ} + 36 0^{\circ} n

x - 6 0^{\circ} = 24 0^{\circ} + 36 0^{\circ} n

حلّ:

x = 36 0^{\circ} n + 30 0^{\circ}

x - 6 0^{\circ} = 24 0^{\circ} + 36 0^{\circ} n

انقل

6 0^{\circ}

إلى الجانب الأيمن

x - 6 0^{\circ} = 24 0^{\circ} + 36 0^{\circ} n

للطرفين

6 0^{\circ}

أضف

x - 6 0^{\circ} + 6 0^{\circ} = 24 0^{\circ} + 36 0^{\circ} n + 6 0^{\circ}

بسّط

x - 6 0^{\circ} + 6 0^{\circ} = 24 0^{\circ} + 36 0^{\circ} n + 6 0^{\circ}

x - 6 0^{\circ} + 6 0^{\circ}

بسّط:

x

x - 6 0^{\circ} + 6 0^{\circ}

- 6 0^{\circ} + 6 0^{\circ} = 0 :

اجمع العناصر المتشابهة

= x

24 0^{\circ} + 36 0^{\circ} n + 6 0^{\circ}

بسّط:

36 0^{\circ} n + 30 0^{\circ}

24 0^{\circ} + 36 0^{\circ} n + 6 0^{\circ}

جمّع التعابير المتشابهة

= 36 0^{\circ} n + 6 0^{\circ} + 24 0^{\circ}

6 0^{\circ} + 24 0^{\circ}

وحّد الكسور:

30 0^{\circ}

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

فعّل القانون

= \frac{18 0 ^{\circ} + 72 0 ^{\circ}}{3}

18 0^{\circ} + 72 0^{\circ} = 90 0^{\circ} :

اجمع العناصر المتشابهة

= 30 0^{\circ}

= 36 0^{\circ} n + 30 0^{\circ}

x = 36 0^{\circ} n + 30 0^{\circ}

x = 36 0^{\circ} n + 30 0^{\circ}

x = 36 0^{\circ} n + 30 0^{\circ}

x - 6 0^{\circ} = 30 0^{\circ} + 36 0^{\circ} n

حلّ:

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

x - 6 0^{\circ} = 30 0^{\circ} + 36 0^{\circ} n

انقل

6 0^{\circ}

إلى الجانب الأيمن

x - 6 0^{\circ} = 30 0^{\circ} + 36 0^{\circ} n

للطرفين

6 0^{\circ}

أضف

x - 6 0^{\circ} + 6 0^{\circ} = 30 0^{\circ} + 36 0^{\circ} n + 6 0^{\circ}

بسّط

x - 6 0^{\circ} + 6 0^{\circ} = 30 0^{\circ} + 36 0^{\circ} n + 6 0^{\circ}

x - 6 0^{\circ} + 6 0^{\circ}

بسّط:

x

x - 6 0^{\circ} + 6 0^{\circ}

- 6 0^{\circ} + 6 0^{\circ} = 0 :

اجمع العناصر المتشابهة

= x

30 0^{\circ} + 36 0^{\circ} n + 6 0^{\circ}

بسّط:

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

30 0^{\circ} + 36 0^{\circ} n + 6 0^{\circ}

جمّع التعابير المتشابهة

= 36 0^{\circ} n + 6 0^{\circ} + 30 0^{\circ}

6 0^{\circ} + 30 0^{\circ}

وحّد الكسور:

36 0^{\circ}

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

فعّل القانون

= \frac{18 0 ^{\circ} + 90 0 ^{\circ}}{3}

18 0^{\circ} + 90 0^{\circ} = 108 0^{\circ} :

اجمع العناصر المتشابهة

= 36 0^{\circ}

\frac{6}{3} = 2 :

اقسم الأعداد

= 36 0^{\circ}

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

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

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

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

x = 36 0^{\circ} n + 30 0^{\circ}, x = 36 0^{\circ} n + 36 0^{\circ}

وحّد الحلول

x = 12 0^{\circ} + 36 0^{\circ} n, x = 36 0^{\circ} n + 18 0^{\circ}, x = 36 0^{\circ} n + 30 0^{\circ}, x = 36 0^{\circ} n + 36 0^{\circ}

رسم

أمثلة شائعة

cos(a)=-4/5 ,90<a<180

cos (a) = - \frac{4}{5}, 9 0^{\circ} < a < 18 0^{\circ}

3cot^2(2x-(3pi)/2)=1

3 cot^{2} (2 x - \frac{3 π}{2}) = 1

1.6sin(θ)=1.49

1.6 sin (θ) = 1.49

cos(x)=0.695

cos (x) = 0.695

sin(2.5x)=2.75cos(2.5x)

sin (2.5 x) = 2.75 cos (2.5 x)