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شائع >

sin(x)-2sin(x)cos(x)=0,0<= x<= 2pi

الحلّ

sin (x) - 2 sin (x) cos (x) = 0, 0 \leq x \leq 2 π

الحلّ

x = 0, x = π, x = 2 π, x = \frac{π}{3}, x = \frac{5 π}{3}

+1

درجات

x = 0^{\circ}, x = 18 0^{\circ}, x = 36 0^{\circ}, x = 6 0^{\circ}, x = 30 0^{\circ}

خطوات الحلّ

sin (x) - 2 sin (x) cos (x) = 0, 0 \leq x \leq 2 π

sin (x) - 2 sin (x) cos (x)

حلل إلى عوامل:

- sin (x) (2 cos (x) - 1)

sin (x) - 2 sin (x) cos (x)

- sin (x)

قم باخراج العامل المشترك

= - sin (x) (- 1 + 2 cos (x))

- sin (x) (2 cos (x) - 1) = 0

حلّ كل جزء على حدة

sin (x) = 0 or 2 cos (x) - 1 = 0

sin (x) = 0, 0 \leq x \leq 2 π : x = 0, x = π, x = 2 π

sin (x) = 0, 0 \leq x \leq 2 π

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

0 \leq x \leq 2 π :

حلول للمدى

x = 0, x = π, x = 2 π

2 cos (x) - 1 = 0, 0 \leq x \leq 2 π : x = \frac{π}{3}, x = \frac{5 π}{3}

2 cos (x) - 1 = 0, 0 \leq x \leq 2 π

انقل

1

إلى الجانب الأيمن

2 cos (x) - 1 = 0

للطرفين

1

أضف

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

بسّط

2 cos (x) = 1

2 cos (x) = 1

2

اقسم الطرفين على

2 cos (x) = 1

2

اقسم الطرفين على

\frac{2 cos ( x )}{2} = \frac{1}{2}

بسّط

cos (x) = \frac{1}{2}

cos (x) = \frac{1}{2}

cos (x) = \frac{1}{2} :

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

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

0 \leq x \leq 2 π :

حلول للمدى

x = \frac{π}{3}, x = \frac{5 π}{3}

وحّد الحلول

x = 0, x = π, x = 2 π, x = \frac{π}{3}, x = \frac{5 π}{3}

رسم

أمثلة شائعة

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

cos (x + π) - cos (x) - 1 = 0

sin (x) = \frac{15}{17}

2cos(x)-sec(x)=1

2 cos (x) - sec (x) = 1

cos(x)tan(x)=5tan(x)

cos (x) tan (x) = 5 tan (x)

- 5 sin (5 x) = 0