ar

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

شائع علم المثلثات >

sin(x)cos(x)=tan(x)

الحلّ

sin (x) cos (x) = tan (x)

الحلّ

x = 2 πn, x = π + 2 πn

+1

درجات

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

خطوات الحلّ

sin (x) cos (x) = tan (x)

من الطرفين

tan (x)

اطرح

sin (x) cos (x) - tan (x) = 0

sin, cos :

عبّر بواسطة

- tan (x) + cos (x) sin (x)

tan (x) = \frac{sin ( x )}{cos ( x )}

:Use the basic trigonometric identity

= - \frac{sin ( x )}{cos ( x )} + cos (x) sin (x)

- \frac{sin ( x )}{cos ( x )} + cos (x) sin (x)

بسّط:

\frac{- sin ( x ) + cos ^{2} ( x ) sin ( x )}{cos ( x )}

- \frac{sin ( x )}{cos ( x )} + cos (x) sin (x)

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

:حوّل الأعداد لكسور

= - \frac{sin ( x )}{cos ( x )} + \frac{cos ( x ) sin ( x ) cos ( x )}{cos ( x )}

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

:بما أنّ المقامات متساوية، اجمع البسوط

= \frac{- sin ( x ) + cos ( x ) sin ( x ) cos ( x )}{cos ( x )}

- sin (x) + cos (x) sin (x) cos (x) = - sin (x) + cos^{2} (x) sin (x)

- sin (x) + cos (x) sin (x) cos (x)

cos (x) sin (x) cos (x) = cos^{2} (x) sin (x)

cos (x) sin (x) cos (x)

a^{b} \cdot a^{c} = a^{b + c}

:فعّل قانون القوى

cos (x) cos (x) = cos^{1 + 1} (x)

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

1 + 1 = 2 :

اجمع الأعداد

= sin (x) cos^{2} (x)

= - sin (x) + cos^{2} (x) sin (x)

= \frac{- sin ( x ) + cos ^{2} ( x ) sin ( x )}{cos ( x )}

= \frac{- sin ( x ) + cos ^{2} ( x ) sin ( x )}{cos ( x )}

\frac{- sin ( x ) + cos ^{2} ( x ) sin ( x )}{cos ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

- sin (x) + cos^{2} (x) sin (x)

حلل إلى عوامل:

sin (x) (cos (x) + 1) (cos (x) - 1)

- sin (x) + cos^{2} (x) sin (x)

sin (x)

قم باخراج العامل المشترك

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

cos^{2} (x) - 1

حلل إلى عوامل:

(cos (x) + 1) (cos (x) - 1)

cos^{2} (x) - 1

1^{2}

كـ

1

اكتب مجددًا

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

x^{2} - y^{2} = (x + y) (x - y)

فعّل قانون فرق المربّعات

cos^{2} (x) - 1^{2} = (cos (x) + 1) (cos (x) - 1)

= (cos (x) + 1) (cos (x) - 1)

= sin (x) (cos (x) + 1) (cos (x) - 1)

sin (x) (cos (x) + 1) (cos (x) - 1) = 0

حلّ كل جزء على حدة

sin (x) = 0 or cos (x) + 1 = 0 or cos (x) - 1 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 0

sin (x) = 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}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn

حلّ:

x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

cos (x) + 1 = 0 : x = π + 2 πn

cos (x) + 1 = 0

انقل

1

إلى الجانب الأيمن

cos (x) + 1 = 0

من الطرفين

1

اطرح

cos (x) + 1 - 1 = 0 - 1

بسّط

cos (x) = - 1

cos (x) = - 1

cos (x) = - 1 :

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}

x = π + 2 πn

x = π + 2 πn

cos (x) - 1 = 0 : x = 2 πn

cos (x) - 1 = 0

انقل

1

إلى الجانب الأيمن

cos (x) - 1 = 0

للطرفين

1

أضف

cos (x) - 1 + 1 = 0 + 1

بسّط

cos (x) = 1

cos (x) = 1

cos (x) = 1 :

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}

x = 0 + 2 πn

x = 0 + 2 πn

x = 0 + 2 πn

حلّ:

x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn

وحّد الحلول

x = 2 πn, x = π + 2 πn

رسم

أمثلة شائعة

cos(x)=(sqrt(2))/4

cos (x) = \frac{2}{4}

sin(x)-sin(x)*cos(x)=0

sin (x) - sin (x) \cdot cos (x) = 0

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

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

10tan(θ)-4.9((10)/(13cos(θ)))^2=0

10 tan (θ) - 4.9 (\frac{10}{13 cos ( θ )})^{2} = 0

1-cos^2(θ)-6959cos(θ)=0

1 - cos^{2} (θ) - 6959 cos (θ) = 0