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شائع علم المثلثات >

solvefor c,e=r(sec(c/2)-1)

الحلّ

solvefor

الحلّ

c = 2 arcsec (\frac{e}{r} + 1) + 4 πn, c = - 2 arcsec (\frac{e}{r} + 1) + 4 πn

خطوات الحلّ

e = r (sec (\frac{c}{2}) - 1)

بدّل الأطراف

r (sec (\frac{c}{2}) - 1) = e

r; r \neq = 0

اقسم الطرفين على

r (sec (\frac{c}{2}) - 1) = e

r; r \neq = 0

اقسم الطرفين على

\frac{r ( sec ( \frac{c}{2} ) - 1 )}{r} = \frac{e}{r}; r \neq = 0

بسّط

sec (\frac{c}{2}) - 1 = \frac{e}{r}; r \neq = 0

sec (\frac{c}{2}) - 1 = \frac{e}{r}; r \neq = 0

انقل

1

إلى الجانب الأيمن

sec (\frac{c}{2}) - 1 = \frac{e}{r}; r \neq = 0

للطرفين

1

أضف

sec (\frac{c}{2}) - 1 + 1 = \frac{e}{r} + 1; r \neq = 0

بسّط

sec (\frac{c}{2}) = \frac{e}{r} + 1; r \neq = 0

sec (\frac{c}{2}) = \frac{e}{r} + 1; r \neq = 0

Apply trig inverse properties

sec (\frac{c}{2}) = \frac{e}{r} + 1

sec (\frac{c}{2}) = \frac{e}{r} + 1 :

حلول عامّة لـ

sec (x) = a \Rightarrow x = arcsec (a) + 2 πn, x = - arcsec (a) + 2 πn

\frac{c}{2} = arcsec (\frac{e}{r} + 1) + 2 πn, \frac{c}{2} = - arcsec (\frac{e}{r} + 1) + 2 πn

\frac{c}{2} = arcsec (\frac{e}{r} + 1) + 2 πn, \frac{c}{2} = - arcsec (\frac{e}{r} + 1) + 2 πn

\frac{c}{2} = arcsec (\frac{e}{r} + 1) + 2 πn

حلّ:

c = 2 arcsec (\frac{e}{r} + 1) + 4 πn

\frac{c}{2} = arcsec (\frac{e}{r} + 1) + 2 πn

2

اضرب الطرفين بـ

\frac{c}{2} = arcsec (\frac{e}{r} + 1) + 2 πn

2

اضرب الطرفين بـ

\frac{2 c}{2} = 2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn

بسّط

\frac{2 c}{2} = 2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn

\frac{2 c}{2}

بسّط:

c

\frac{2 c}{2}

\frac{2}{2} = 1 :

اقسم الأعداد

= c

2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn

بسّط:

2 arcsec (\frac{e}{r} + 1) + 4 πn

2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn

2 \cdot 2 = 4 :

اضرب الأعداد

= 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = 2 arcsec (\frac{e}{r} + 1) + 4 πn

\frac{c}{2} = - arcsec (\frac{e}{r} + 1) + 2 πn

حلّ:

c = - 2 arcsec (\frac{e}{r} + 1) + 4 πn

\frac{c}{2} = - arcsec (\frac{e}{r} + 1) + 2 πn

2

اضرب الطرفين بـ

\frac{c}{2} = - arcsec (\frac{e}{r} + 1) + 2 πn

2

اضرب الطرفين بـ

\frac{2 c}{2} = - 2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn

بسّط

\frac{2 c}{2} = - 2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn

\frac{2 c}{2}

بسّط:

c

\frac{2 c}{2}

\frac{2}{2} = 1 :

اقسم الأعداد

= c

- 2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn

بسّط:

- 2 arcsec (\frac{e}{r} + 1) + 4 πn

- 2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn

2 \cdot 2 = 4 :

اضرب الأعداد

= - 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = - 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = - 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = - 2 arcsec (\frac{e}{r} + 1) + 4 πn

c = 2 arcsec (\frac{e}{r} + 1) + 4 πn, c = - 2 arcsec (\frac{e}{r} + 1) + 4 πn

رسم

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