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شائع >

solvefor A,sin(B+C/2)=cos(A/2)

الحلّ

solve for

A, sin (B + \frac{C}{2}) = cos (\frac{A}{2})

الحلّ

A = 2 arccos (sin (B + \frac{C}{2})) + 4 πn, A = - 2 arccos (sin (B + \frac{C}{2})) + 4 πn

خطوات الحلّ

sin (B + \frac{C}{2}) = cos (\frac{A}{2})

بدّل الأطراف

cos (\frac{A}{2}) = sin (B + \frac{C}{2})

Apply trig inverse properties

cos (\frac{A}{2}) = sin (B + \frac{C}{2})

cos (\frac{A}{2}) = sin (B + \frac{C}{2}) :

حلول عامّة لـ

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

\frac{A}{2} = arccos (sin (B + \frac{C}{2})) + 2 πn, \frac{A}{2} = - arccos (sin (B + \frac{C}{2})) + 2 πn

\frac{A}{2} = arccos (sin (B + \frac{C}{2})) + 2 πn, \frac{A}{2} = - arccos (sin (B + \frac{C}{2})) + 2 πn

\frac{A}{2} = arccos (sin (B + \frac{C}{2})) + 2 πn

حلّ:

A = 2 arccos (sin (B + \frac{C}{2})) + 4 πn

\frac{A}{2} = arccos (sin (B + \frac{C}{2})) + 2 πn

2

اضرب الطرفين بـ

\frac{A}{2} = arccos (sin (B + \frac{C}{2})) + 2 πn

2

اضرب الطرفين بـ

\frac{2 A}{2} = 2 arccos (sin (B + \frac{C}{2})) + 2 \cdot 2 πn

بسّط

\frac{2 A}{2} = 2 arccos (sin (B + \frac{C}{2})) + 2 \cdot 2 πn

\frac{2 A}{2}

بسّط:

A

\frac{2 A}{2}

\frac{2}{2} = 1 :

اقسم الأعداد

= A

2 arccos (sin (B + \frac{C}{2})) + 2 \cdot 2 πn

بسّط:

2 arccos (sin (B + \frac{C}{2})) + 4 πn

2 arccos (sin (B + \frac{C}{2})) + 2 \cdot 2 πn

2 \cdot 2 = 4 :

اضرب الأعداد

= 2 arccos (sin (B + \frac{C}{2})) + 4 πn

A = 2 arccos (sin (B + \frac{C}{2})) + 4 πn

A = 2 arccos (sin (B + \frac{C}{2})) + 4 πn

A = 2 arccos (sin (B + \frac{C}{2})) + 4 πn

\frac{A}{2} = - arccos (sin (B + \frac{C}{2})) + 2 πn

حلّ:

A = - 2 arccos (sin (B + \frac{C}{2})) + 4 πn

\frac{A}{2} = - arccos (sin (B + \frac{C}{2})) + 2 πn

2

اضرب الطرفين بـ

\frac{A}{2} = - arccos (sin (B + \frac{C}{2})) + 2 πn

2

اضرب الطرفين بـ

\frac{2 A}{2} = - 2 arccos (sin (B + \frac{C}{2})) + 2 \cdot 2 πn

بسّط

\frac{2 A}{2} = - 2 arccos (sin (B + \frac{C}{2})) + 2 \cdot 2 πn

\frac{2 A}{2}

بسّط:

A

\frac{2 A}{2}

\frac{2}{2} = 1 :

اقسم الأعداد

= A

- 2 arccos (sin (B + \frac{C}{2})) + 2 \cdot 2 πn

بسّط:

- 2 arccos (sin (B + \frac{C}{2})) + 4 πn

- 2 arccos (sin (B + \frac{C}{2})) + 2 \cdot 2 πn

2 \cdot 2 = 4 :

اضرب الأعداد

= - 2 arccos (sin (B + \frac{C}{2})) + 4 πn

A = - 2 arccos (sin (B + \frac{C}{2})) + 4 πn

A = - 2 arccos (sin (B + \frac{C}{2})) + 4 πn

A = - 2 arccos (sin (B + \frac{C}{2})) + 4 πn

A = 2 arccos (sin (B + \frac{C}{2})) + 4 πn, A = - 2 arccos (sin (B + \frac{C}{2})) + 4 πn

رسم

أمثلة شائعة

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7-2sin(5(x+pi/8))=9

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