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Popular Trigonometria >

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

Solução

solvefor

Solução

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

Passos da solução

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

Trocar lados

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

Dividir ambos os lados por

r; r \neq = 0

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

Dividir ambos os lados por

r; r \neq = 0

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

Simplificar

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

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

Mova

1

para o lado direito

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

Adicionar

1

a ambos os lados

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

Simplificar

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

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

Aplique as propriedades trigonométricas inversas

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

Soluções gerais para

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

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

Resolver

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

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

Multiplicar ambos os lados por

2

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

Multiplicar ambos os lados por

2

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

Simplificar

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

Simplificar

\frac{2 c}{2} : c

\frac{2 c}{2}

Dividir:

\frac{2}{2} = 1

= c

Simplificar

2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn : 2 arcsec (\frac{e}{r} + 1) + 4 πn

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

Multiplicar os números:

2 \cdot 2 = 4

= 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

Resolver

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

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

Multiplicar ambos os lados por

2

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

Multiplicar ambos os lados por

2

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

Simplificar

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

Simplificar

\frac{2 c}{2} : c

\frac{2 c}{2}

Dividir:

\frac{2}{2} = 1

= c

Simplificar

- 2 arcsec (\frac{e}{r} + 1) + 2 \cdot 2 πn : - 2 arcsec (\frac{e}{r} + 1) + 4 πn

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

Multiplicar os números:

2 \cdot 2 = 4

= - 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

Gráfico

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