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solvefor g,θ=arctan((5.54)/(10g)+0.2)

Solução

resolver para

g, θ = arctan (\frac{5.54}{10 g} + 0.2)

g = \frac{5.54}{10 ( tan ( θ ) - 0.2 )}

Passos da solução

θ = arctan (\frac{5.54}{10 g} + 0.2)

Trocar lados

arctan (\frac{5.54}{10 g} + 0.2) = θ

Aplique as propriedades trigonométricas inversas

arctan (\frac{5.54}{10 g} + 0.2) = θ

arctan (x) = a \Rightarrow x = tan (a)

\frac{5.54}{10 g} + 0.2 = tan (θ)

\frac{5.54}{10 g} + 0.2 = tan (θ)

Resolver

\frac{5.54}{10 g} + 0.2 = tan (θ) : g = \frac{5.54}{10 ( tan ( θ ) - 0.2 )}; θ \neq = 0.19739 \dots + πn

\frac{5.54}{10 g} + 0.2 = tan (θ)

Mova

0.2

para o lado direito

\frac{5.54}{10 g} + 0.2 = tan (θ)

Subtrair

0.2

de ambos os lados

\frac{5.54}{10 g} + 0.2 - 0.2 = tan (θ) - 0.2

Simplificar

\frac{5.54}{10 g} = tan (θ) - 0.2

\frac{5.54}{10 g} = tan (θ) - 0.2

Multiplicar ambos os lados por

g

\frac{5.54}{10 g} = tan (θ) - 0.2

Multiplicar ambos os lados por

g

\frac{5.54}{10 g} g = tan (θ) g - 0.2 g

Simplificar

\frac{5.54}{10} = tan (θ) g - 0.2 g

\frac{5.54}{10} = tan (θ) g - 0.2 g

Trocar lados

tan (θ) g - 0.2 g = \frac{5.54}{10}

Fatorar

tan (θ) g - 0.2 g : g (tan (θ) - 0.2)

tan (θ) g - 0.2 g

Fatorar o termo comum

g

= g (tan (θ) - 0.2)

g (tan (θ) - 0.2) = \frac{5.54}{10}

Dividir ambos os lados por

tan (θ) - 0.2; θ \neq = 0.19739 \dots + πn

g (tan (θ) - 0.2) = \frac{5.54}{10}

Dividir ambos os lados por

tan (θ) - 0.2; θ \neq = 0.19739 \dots + πn

\frac{g ( tan ( θ ) - 0.2 )}{tan ( θ ) - 0.2} = \frac{\frac{5.54}{10}}{tan ( θ ) - 0.2}; θ \neq = 0.19739 \dots + πn

Simplificar

\frac{g ( tan ( θ ) - 0.2 )}{tan ( θ ) - 0.2} = \frac{\frac{5.54}{10}}{tan ( θ ) - 0.2}

Simplificar

\frac{g ( tan ( θ ) - 0.2 )}{tan ( θ ) - 0.2} : g

\frac{g ( tan ( θ ) - 0.2 )}{tan ( θ ) - 0.2}

Eliminar o fator comum:

tan (θ) - 0.2

= g

Simplificar

\frac{\frac{5.54}{10}}{tan ( θ ) - 0.2} : \frac{5.54}{10 ( tan ( θ ) - 0.2 )}

\frac{\frac{5.54}{10}}{tan ( θ ) - 0.2}

Aplicar as propriedades das frações:

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

= \frac{5.54}{10 ( tan ( θ ) - 0.2 )}

g = \frac{5.54}{10 ( tan ( θ ) - 0.2 )}; θ \neq = 0.19739 \dots + πn

g = \frac{5.54}{10 ( tan ( θ ) - 0.2 )}; θ \neq = 0.19739 \dots + πn

g = \frac{5.54}{10 ( tan ( θ ) - 0.2 )}; θ \neq = 0.19739 \dots + πn

g = \frac{5.54}{10 ( tan ( θ ) - 0.2 )}