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Popular Trigonometria >

solvefor x,y=3cos(fxx+pi/2)+5

Solução

resolver para

x, y = 3 cos (f xx + \frac{π}{2}) + 5

Solução

x = \frac{2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}, x = - \frac{2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}, x = \frac{- 2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}, x = - \frac{- 2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}

Passos da solução

y = 3 cos (f xx + \frac{π}{2}) + 5

Trocar lados

3 cos (f xx + \frac{π}{2}) + 5 = y

Mova

5

para o lado direito

3 cos (f xx + \frac{π}{2}) + 5 = y

Subtrair

5

de ambos os lados

3 cos (f xx + \frac{π}{2}) + 5 - 5 = y - 5

Simplificar

3 cos (f xx + \frac{π}{2}) = y - 5

3 cos (f xx + \frac{π}{2}) = y - 5

Dividir ambos os lados por

3

3 cos (f xx + \frac{π}{2}) = y - 5

Dividir ambos os lados por

3

\frac{3 cos ( f xx + \frac{π}{2} )}{3} = \frac{y}{3} - \frac{5}{3}

Simplificar

\frac{3 cos ( f xx + \frac{π}{2} )}{3} = \frac{y}{3} - \frac{5}{3}

Simplificar

\frac{3 cos ( f xx + \frac{π}{2} )}{3} : cos (f xx + \frac{π}{2})

\frac{3 cos ( f xx + \frac{π}{2} )}{3}

Dividir:

\frac{3}{3} = 1

= cos (f xx + \frac{π}{2})

Simplificar

\frac{y}{3} - \frac{5}{3} : \frac{y - 5}{3}

\frac{y}{3} - \frac{5}{3}

Aplicar a regra

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

= \frac{y - 5}{3}

cos (f xx + \frac{π}{2}) = \frac{y - 5}{3}

cos (f xx + \frac{π}{2}) = \frac{y - 5}{3}

cos (f xx + \frac{π}{2}) = \frac{y - 5}{3}

Aplique as propriedades trigonométricas inversas

cos (f xx + \frac{π}{2}) = \frac{y - 5}{3}

Soluções gerais para

cos (f xx + \frac{π}{2}) = \frac{y - 5}{3}

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

f xx + \frac{π}{2} = arccos (\frac{y - 5}{3}) + 2 πn, f xx + \frac{π}{2} = - arccos (\frac{y - 5}{3}) + 2 πn

f xx + \frac{π}{2} = arccos (\frac{y - 5}{3}) + 2 πn, f xx + \frac{π}{2} = - arccos (\frac{y - 5}{3}) + 2 πn

Resolver

f xx + \frac{π}{2} = arccos (\frac{y - 5}{3}) + 2 πn : x = \frac{2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}, x = - \frac{2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}; f \neq = 0

f xx + \frac{π}{2} = arccos (\frac{y - 5}{3}) + 2 πn

Mova

\frac{π}{2}

para o lado direito

f xx + \frac{π}{2} = arccos (\frac{y - 5}{3}) + 2 πn

Subtrair

\frac{π}{2}

de ambos os lados

f xx + \frac{π}{2} - \frac{π}{2} = arccos (\frac{y - 5}{3}) + 2 πn - \frac{π}{2}

Simplificar

f xx = arccos (\frac{y - 5}{3}) + 2 πn - \frac{π}{2}

f xx = arccos (\frac{y - 5}{3}) + 2 πn - \frac{π}{2}

Simplificar

x^{2} f = arccos (\frac{y - 5}{3}) + 2 πn - \frac{π}{2}

Dividir ambos os lados por

f; f \neq = 0

\frac{x ^{2} f}{f} = \frac{arccos ( \frac{y - 5}{3} ) + 2 πn - \frac{π}{2}}{f}; f \neq = 0

x^{2} = \frac{2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}; f \neq = 0

Para

x^{2} = f (a)

as soluções são

x = f (a), - f (a)

x = \frac{2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}, x = - \frac{2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}; f \neq = 0

Resolver

f xx + \frac{π}{2} = - arccos (\frac{y - 5}{3}) + 2 πn : x = \frac{- 2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}, x = - \frac{- 2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}; f \neq = 0

f xx + \frac{π}{2} = - arccos (\frac{y - 5}{3}) + 2 πn

Mova

\frac{π}{2}

para o lado direito

f xx + \frac{π}{2} = - arccos (\frac{y - 5}{3}) + 2 πn

Subtrair

\frac{π}{2}

de ambos os lados

f xx + \frac{π}{2} - \frac{π}{2} = - arccos (\frac{y - 5}{3}) + 2 πn - \frac{π}{2}

Simplificar

f xx = - arccos (\frac{y - 5}{3}) + 2 πn - \frac{π}{2}

f xx = - arccos (\frac{y - 5}{3}) + 2 πn - \frac{π}{2}

Simplificar

x^{2} f = - arccos (\frac{y - 5}{3}) + 2 πn - \frac{π}{2}

Dividir ambos os lados por

f; f \neq = 0

\frac{x ^{2} f}{f} = \frac{- arccos ( \frac{y - 5}{3} ) + 2 πn - \frac{π}{2}}{f}; f \neq = 0

x^{2} = \frac{- 2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}; f \neq = 0

Para

x^{2} = f (a)

as soluções são

x = f (a), - f (a)

x = \frac{- 2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}, x = - \frac{- 2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}; f \neq = 0

x = \frac{2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}, x = - \frac{2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}, x = \frac{- 2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}, x = - \frac{- 2 arccos ( \frac{y - 5}{3} ) + 4 πn - π}{2 f}

Gráfico

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