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شائع علم المثلثات >

-3sqrt(3)+7csc(θ/5+23)=5sqrt(3)

الحلّ

- 33 + 7 csc (\frac{θ}{5} + 2 3^{\circ}) = 53

الحلّ

θ = 5 \cdot 0.52959 \dots + 180 0^{\circ} n - 11 5^{\circ}, θ = 90 0^{\circ} - 5 \cdot 0.52959 \dots + 180 0^{\circ} n - 11 5^{\circ}

+1

راديان

θ = 5 \cdot 0.52959 \dots - \frac{23 π}{36} + 10 πn, θ = 5 π - 5 \cdot 0.52959 \dots - \frac{23 π}{36} + 10 πn

خطوات الحلّ

- 33 + 7 csc (\frac{θ}{5} + 2 3^{\circ}) = 53

انقل

33

إلى الجانب الأيمن

- 33 + 7 csc (\frac{θ}{5} + 2 3^{\circ}) = 53

للطرفين

33

أضف

- 33 + 7 csc (\frac{θ}{5} + 2 3^{\circ}) + 33 = 53 + 33

بسّط

- 33 + 7 csc (\frac{θ}{5} + 2 3^{\circ}) + 33 = 53 + 33

- 33 + 7 csc (\frac{θ}{5} + 2 3^{\circ}) + 33

بسّط:

7 csc (\frac{θ}{5} + 2 3^{\circ})

- 33 + 7 csc (\frac{θ}{5} + 2 3^{\circ}) + 33

- 33 + 33 = 0 :

اجمع العناصر المتشابهة

= 7 csc (\frac{θ}{5} + 2 3^{\circ})

53 + 33

بسّط:

83

53 + 33

53 + 33 = 83 :

اجمع العناصر المتشابهة

= 83

7 csc (\frac{θ}{5} + 2 3^{\circ}) = 83

7 csc (\frac{θ}{5} + 2 3^{\circ}) = 83

7 csc (\frac{θ}{5} + 2 3^{\circ}) = 83

7

اقسم الطرفين على

7 csc (\frac{θ}{5} + 2 3^{\circ}) = 83

7

اقسم الطرفين على

\frac{7 csc ( \frac{θ}{5} + 2 3 ^{\circ} )}{7} = \frac{8 3}{7}

بسّط

csc (\frac{θ}{5} + 2 3^{\circ}) = \frac{8 3}{7}

csc (\frac{θ}{5} + 2 3^{\circ}) = \frac{8 3}{7}

Apply trig inverse properties

csc (\frac{θ}{5} + 2 3^{\circ}) = \frac{8 3}{7}

csc (\frac{θ}{5} + 2 3^{\circ}) = \frac{8 3}{7} :

حلول عامّة لـ

csc (x) = a \Rightarrow x = arccsc (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arccsc (a) + 36 0^{\circ} n

\frac{θ}{5} + 2 3^{\circ} = arccsc (\frac{8 3}{7}) + 36 0^{\circ} n, \frac{θ}{5} + 2 3^{\circ} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n

\frac{θ}{5} + 2 3^{\circ} = arccsc (\frac{8 3}{7}) + 36 0^{\circ} n, \frac{θ}{5} + 2 3^{\circ} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n

\frac{θ}{5} + 2 3^{\circ} = arccsc (\frac{8 3}{7}) + 36 0^{\circ} n

حلّ:

θ = 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

\frac{θ}{5} + 2 3^{\circ} = arccsc (\frac{8 3}{7}) + 36 0^{\circ} n

انقل

2 3^{\circ}

إلى الجانب الأيمن

\frac{θ}{5} + 2 3^{\circ} = arccsc (\frac{8 3}{7}) + 36 0^{\circ} n

من الطرفين

2 3^{\circ}

اطرح

\frac{θ}{5} + 2 3^{\circ} - 2 3^{\circ} = arccsc (\frac{8 3}{7}) + 36 0^{\circ} n - 2 3^{\circ}

بسّط

\frac{θ}{5} = arccsc (\frac{8 3}{7}) + 36 0^{\circ} n - 2 3^{\circ}

\frac{θ}{5} = arccsc (\frac{8 3}{7}) + 36 0^{\circ} n - 2 3^{\circ}

5

اضرب الطرفين بـ

\frac{θ}{5} = arccsc (\frac{8 3}{7}) + 36 0^{\circ} n - 2 3^{\circ}

5

اضرب الطرفين بـ

\frac{5 θ}{5} = 5 arccsc (\frac{8 3}{7}) + 5 \cdot 36 0^{\circ} n - 5 \cdot 2 3^{\circ}

بسّط

\frac{5 θ}{5} = 5 arccsc (\frac{8 3}{7}) + 5 \cdot 36 0^{\circ} n - 5 \cdot 2 3^{\circ}

\frac{5 θ}{5}

بسّط:

θ

\frac{5 θ}{5}

\frac{5}{5} = 1 :

اقسم الأعداد

= θ

5 arccsc (\frac{8 3}{7}) + 5 \cdot 36 0^{\circ} n - 5 \cdot 2 3^{\circ}

بسّط:

5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

5 arccsc (\frac{8 3}{7}) + 5 \cdot 36 0^{\circ} n - 5 \cdot 2 3^{\circ}

5 \cdot 36 0^{\circ} n = 180 0^{\circ} n

5 \cdot 36 0^{\circ} n

5 \cdot 2 = 10 :

اضرب الأعداد

= 180 0^{\circ} n

5 \cdot 2 3^{\circ} = 11 5^{\circ}

5 \cdot 2 3^{\circ}

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

:اضرب كسور

= 11 5^{\circ}

23 \cdot 5 = 115 :

اضرب الأعداد

= 11 5^{\circ}

5 :

إلغ العوامل المشتركة

= 11 5^{\circ}

= 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

θ = 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

θ = 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

θ = 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

\frac{θ}{5} + 2 3^{\circ} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n

حلّ:

θ = 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

\frac{θ}{5} + 2 3^{\circ} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n

انقل

2 3^{\circ}

إلى الجانب الأيمن

\frac{θ}{5} + 2 3^{\circ} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n

من الطرفين

2 3^{\circ}

اطرح

\frac{θ}{5} + 2 3^{\circ} - 2 3^{\circ} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n - 2 3^{\circ}

بسّط

\frac{θ}{5} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n - 2 3^{\circ}

\frac{θ}{5} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n - 2 3^{\circ}

5

اضرب الطرفين بـ

\frac{θ}{5} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n - 2 3^{\circ}

5

اضرب الطرفين بـ

\frac{5 θ}{5} = 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 5 \cdot 36 0^{\circ} n - 5 \cdot 2 3^{\circ}

بسّط

\frac{5 θ}{5} = 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 5 \cdot 36 0^{\circ} n - 5 \cdot 2 3^{\circ}

\frac{5 θ}{5}

بسّط:

θ

\frac{5 θ}{5}

\frac{5}{5} = 1 :

اقسم الأعداد

= θ

90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 5 \cdot 36 0^{\circ} n - 5 \cdot 2 3^{\circ}

بسّط:

90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 5 \cdot 36 0^{\circ} n - 5 \cdot 2 3^{\circ}

5 \cdot 36 0^{\circ} n = 180 0^{\circ} n

5 \cdot 36 0^{\circ} n

5 \cdot 2 = 10 :

اضرب الأعداد

= 180 0^{\circ} n

5 \cdot 2 3^{\circ} = 11 5^{\circ}

5 \cdot 2 3^{\circ}

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

:اضرب كسور

= 11 5^{\circ}

23 \cdot 5 = 115 :

اضرب الأعداد

= 11 5^{\circ}

5 :

إلغ العوامل المشتركة

= 11 5^{\circ}

= 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

θ = 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

θ = 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

θ = 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

θ = 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}, θ = 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

أظهر الحلّ بالتمثيل العشريّ

θ = 5 \cdot 0.52959 \dots + 180 0^{\circ} n - 11 5^{\circ}, θ = 90 0^{\circ} - 5 \cdot 0.52959 \dots + 180 0^{\circ} n - 11 5^{\circ}

رسم

أمثلة شائعة

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