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شائع علم المثلثات >

(csc(x)+2)(csc(x)-sqrt(2))=0,0<= x<= 2pi

الحلّ

(csc (x) + 2) (csc (x) - 2) = 0, 0 \leq x \leq 2 π

الحلّ

x = \frac{7 π}{6}, x = \frac{11 π}{6}, x = \frac{π}{4}, x = \frac{3 π}{4}

+1

درجات

x = 21 0^{\circ}, x = 33 0^{\circ}, x = 4 5^{\circ}, x = 13 5^{\circ}

خطوات الحلّ

(csc (x) + 2) (csc (x) - 2) = 0, 0 \leq x \leq 2 π

حلّ كل جزء على حدة

csc (x) + 2 = 0 or csc (x) - 2 = 0

csc (x) + 2 = 0, 0 \leq x \leq 2 π : x = \frac{7 π}{6}, x = \frac{11 π}{6}

csc (x) + 2 = 0, 0 \leq x \leq 2 π

انقل

2

إلى الجانب الأيمن

csc (x) + 2 = 0

من الطرفين

2

اطرح

csc (x) + 2 - 2 = 0 - 2

بسّط

csc (x) = - 2

csc (x) = - 2

csc (x) = - 2 :

حلول عامّة لـ

csc (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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 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} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

0 \leq x \leq 2 π :

حلول للمدى

x = \frac{7 π}{6}, x = \frac{11 π}{6}

csc (x) - 2 = 0, 0 \leq x \leq 2 π : x = \frac{π}{4}, x = \frac{3 π}{4}

csc (x) - 2 = 0, 0 \leq x \leq 2 π

انقل

2

إلى الجانب الأيمن

csc (x) - 2 = 0

للطرفين

2

أضف

csc (x) - 2 + 2 = 0 + 2

بسّط

csc (x) = 2

csc (x) = 2

csc (x) = 2 :

حلول عامّة لـ

csc (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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 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} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

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

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

0 \leq x \leq 2 π :

حلول للمدى

x = \frac{π}{4}, x = \frac{3 π}{4}

وحّد الحلول

x = \frac{7 π}{6}, x = \frac{11 π}{6}, x = \frac{π}{4}, x = \frac{3 π}{4}

رسم

أمثلة شائعة

cos (x) = 55

cos (x) = 35

sin (x) = \frac{12}{10}

cos (x) = 45

(51)/(sin(93))=(43)/(sin(C))

\frac{51}{sin ( 9 3 ^{\circ} )} = \frac{43}{sin ( C )}