ar

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

شائع علم المثلثات >

cos(x/4)sin(x/4)=sqrt(3)sin(x/4)cos(x/4)

الحلّ

cos (\frac{x}{4}) sin (\frac{x}{4}) = 3 sin (\frac{x}{4}) cos (\frac{x}{4})

الحلّ

x = 2 π + 8 πn, x = 6 π + 8 πn, x = 8 πn, x = 4 π + 8 πn

+1

درجات

x = 36 0^{\circ} + 144 0^{\circ} n, x = 108 0^{\circ} + 144 0^{\circ} n, x = 0^{\circ} + 144 0^{\circ} n, x = 72 0^{\circ} + 144 0^{\circ} n

خطوات الحلّ

cos (\frac{x}{4}) sin (\frac{x}{4}) = 3 sin (\frac{x}{4}) cos (\frac{x}{4})

من الطرفين

3 sin (\frac{x}{4}) cos (\frac{x}{4})

اطرح

cos (\frac{x}{4}) sin (\frac{x}{4}) - 3 sin (\frac{x}{4}) cos (\frac{x}{4}) = 0

cos (\frac{x}{4}) sin (\frac{x}{4}) - 3 sin (\frac{x}{4}) cos (\frac{x}{4})

حلل إلى عوامل:

(1 - 3) cos (\frac{x}{4}) sin (\frac{x}{4})

cos (\frac{x}{4}) sin (\frac{x}{4}) - 3 sin (\frac{x}{4}) cos (\frac{x}{4})

cos (\frac{x}{4}) sin (\frac{x}{4})

قم باخراج العامل المشترك

= cos (\frac{x}{4}) sin (\frac{x}{4}) (1 - 3)

(1 - 3) cos (\frac{x}{4}) sin (\frac{x}{4}) = 0

حلّ كل جزء على حدة

cos (\frac{x}{4}) = 0 or sin (\frac{x}{4}) = 0

cos (\frac{x}{4}) = 0 : x = 2 π + 8 πn, x = 6 π + 8 πn

cos (\frac{x}{4}) = 0

cos (\frac{x}{4}) = 0 :

حلول عامّة لـ

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

\frac{x}{4} = \frac{π}{2} + 2 πn, \frac{x}{4} = \frac{3 π}{2} + 2 πn

\frac{x}{4} = \frac{π}{2} + 2 πn, \frac{x}{4} = \frac{3 π}{2} + 2 πn

\frac{x}{4} = \frac{π}{2} + 2 πn

حلّ:

x = 2 π + 8 πn

\frac{x}{4} = \frac{π}{2} + 2 πn

4

اضرب الطرفين بـ

\frac{x}{4} = \frac{π}{2} + 2 πn

4

اضرب الطرفين بـ

\frac{4 x}{4} = 4 \cdot \frac{π}{2} + 4 \cdot 2 πn

بسّط

\frac{4 x}{4} = 4 \cdot \frac{π}{2} + 4 \cdot 2 πn

\frac{4 x}{4}

بسّط:

x

\frac{4 x}{4}

\frac{4}{4} = 1 :

اقسم الأعداد

= x

4 \cdot \frac{π}{2} + 4 \cdot 2 πn

بسّط:

2 π + 8 πn

4 \cdot \frac{π}{2} + 4 \cdot 2 πn

4 \cdot \frac{π}{2} = 2 π

4 \cdot \frac{π}{2}

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

:اضرب كسور

= \frac{π 4}{2}

\frac{4}{2} = 2 :

اقسم الأعداد

= 2 π

4 \cdot 2 πn = 8 πn

4 \cdot 2 πn

4 \cdot 2 = 8 :

اضرب الأعداد

= 8 πn

= 2 π + 8 πn

x = 2 π + 8 πn

x = 2 π + 8 πn

x = 2 π + 8 πn

\frac{x}{4} = \frac{3 π}{2} + 2 πn

حلّ:

x = 6 π + 8 πn

\frac{x}{4} = \frac{3 π}{2} + 2 πn

4

اضرب الطرفين بـ

\frac{x}{4} = \frac{3 π}{2} + 2 πn

4

اضرب الطرفين بـ

\frac{4 x}{4} = 4 \cdot \frac{3 π}{2} + 4 \cdot 2 πn

بسّط

\frac{4 x}{4} = 4 \cdot \frac{3 π}{2} + 4 \cdot 2 πn

\frac{4 x}{4}

بسّط:

x

\frac{4 x}{4}

\frac{4}{4} = 1 :

اقسم الأعداد

= x

4 \cdot \frac{3 π}{2} + 4 \cdot 2 πn

بسّط:

6 π + 8 πn

4 \cdot \frac{3 π}{2} + 4 \cdot 2 πn

4 \cdot \frac{3 π}{2} = 6 π

4 \cdot \frac{3 π}{2}

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

:اضرب كسور

= \frac{3 π 4}{2}

3 \cdot 4 = 12 :

اضرب الأعداد

= \frac{12 π}{2}

\frac{12}{2} = 6 :

اقسم الأعداد

= 6 π

4 \cdot 2 πn = 8 πn

4 \cdot 2 πn

4 \cdot 2 = 8 :

اضرب الأعداد

= 8 πn

= 6 π + 8 πn

x = 6 π + 8 πn

x = 6 π + 8 πn

x = 6 π + 8 πn

x = 2 π + 8 πn, x = 6 π + 8 πn

sin (\frac{x}{4}) = 0 : x = 8 πn, x = 4 π + 8 πn

sin (\frac{x}{4}) = 0

sin (\frac{x}{4}) = 0 :

حلول عامّة لـ

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

\frac{x}{4} = 0 + 2 πn, \frac{x}{4} = π + 2 πn

\frac{x}{4} = 0 + 2 πn, \frac{x}{4} = π + 2 πn

\frac{x}{4} = 0 + 2 πn

حلّ:

x = 8 πn

\frac{x}{4} = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{x}{4} = 2 πn

4

اضرب الطرفين بـ

\frac{x}{4} = 2 πn

4

اضرب الطرفين بـ

\frac{4 x}{4} = 4 \cdot 2 πn

بسّط

x = 8 πn

x = 8 πn

\frac{x}{4} = π + 2 πn

حلّ:

x = 4 π + 8 πn

\frac{x}{4} = π + 2 πn

4

اضرب الطرفين بـ

\frac{x}{4} = π + 2 πn

4

اضرب الطرفين بـ

\frac{4 x}{4} = 4 π + 4 \cdot 2 πn

بسّط

x = 4 π + 8 πn

x = 4 π + 8 πn

x = 8 πn, x = 4 π + 8 πn

وحّد الحلول

x = 2 π + 8 πn, x = 6 π + 8 πn, x = 8 πn, x = 4 π + 8 πn

رسم

أمثلة شائعة

5cos(x)=1+2sin^2(x)

5 cos (x) = 1 + 2 sin^{2} (x)

tan(2x+1)=-cot(x+3)

tan (2 x + 1) = - cot (x + 3)

(4sec^2(x))/2 =-8sec(x)

\frac{4 sec ^{2} ( x )}{2} = - 8 sec (x)

tan(x)+tan^3(x)=0

tan (x) + tan^{3} (x) = 0

sin^3(x)-2sin(x)=4cos^2(x)-3

sin^{3} (x) - 2 sin (x) = 4 cos^{2} (x) - 3