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solvefor y,arctan(y)+1/2 (1-t)^2=c

Solução

resolver para

y, arctan (y) + \frac{1}{2} (1 - t)^{2} = c

y = tan (c - \frac{1}{2} + t - \frac{1}{2} t^{2})

Passos da solução

arctan (y) + \frac{1}{2} (1 - t)^{2} = c

Mova

\frac{1}{2} (1 - t)^{2}

para o lado direito

arctan (y) + \frac{1}{2} (1 - t)^{2} = c

Subtrair

\frac{1}{2} (1 - t)^{2}

de ambos os lados

arctan (y) + \frac{1}{2} (1 - t)^{2} - \frac{1}{2} (1 - t)^{2} = c - \frac{1}{2} (1 - t)^{2}

Simplificar

arctan (y) + \frac{1}{2} (1 - t)^{2} - \frac{1}{2} (1 - t)^{2} = c - \frac{1}{2} (1 - t)^{2}

Simplificar

arctan (y) + \frac{1}{2} (1 - t)^{2} - \frac{1}{2} (1 - t)^{2} : arctan (y)

arctan (y) + \frac{1}{2} (1 - t)^{2} - \frac{1}{2} (1 - t)^{2}

Somar elementos similares:

\frac{1}{2} (1 - t)^{2} - \frac{1}{2} (1 - t)^{2} = 0

= arctan (y)

Simplificar

c - \frac{1}{2} (1 - t)^{2} : c - \frac{1}{2} + t - \frac{1}{2} t^{2}

c - \frac{1}{2} (1 - t)^{2}

(1 - t)^{2} : 1 - 2 t + t^{2}

Aplique a fórmula do quadrado perfeito:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

a = 1, b = t

= 1^{2} - 2 \cdot 1 \cdot t + t^{2}

Simplificar

1^{2} - 2 \cdot 1 \cdot t + t^{2} : 1 - 2 t + t^{2}

1^{2} - 2 \cdot 1 \cdot t + t^{2}

Aplicar a regra

1^{a} = 1

1^{2} = 1

= 1 - 2 \cdot 1 \cdot t + t^{2}

Multiplicar os números:

2 \cdot 1 = 2

= 1 - 2 t + t^{2}

= 1 - 2 t + t^{2}

= c - \frac{1}{2} (1 - 2 t + t^{2})

Expandir

- \frac{1}{2} (1 - 2 t + t^{2}) : - \frac{1}{2} + t - \frac{1}{2} t^{2}

- \frac{1}{2} (1 - 2 t + t^{2})

Aplicar a seguinte regra dos produtos notáveis

= (- \frac{1}{2}) \cdot 1 + (- \frac{1}{2}) (- 2 t) + (- \frac{1}{2}) t^{2}

Aplicar as regras dos sinais

+ (- a) = - a, (- a) (- b) = ab

= - 1 \cdot \frac{1}{2} + 2 \cdot \frac{1}{2} t - \frac{1}{2} t^{2}

Simplificar

- 1 \cdot \frac{1}{2} + 2 \cdot \frac{1}{2} t - \frac{1}{2} t^{2} : - \frac{1}{2} + t - \frac{1}{2} t^{2}

- 1 \cdot \frac{1}{2} + 2 \cdot \frac{1}{2} t - \frac{1}{2} t^{2}

1 \cdot \frac{1}{2} = \frac{1}{2}

1 \cdot \frac{1}{2}

Multiplicar:

1 \cdot \frac{1}{2} = \frac{1}{2}

= \frac{1}{2}

2 \cdot \frac{1}{2} t = t

2 \cdot \frac{1}{2} t

Multiplicar frações:

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

= \frac{1 \cdot 2}{2} t

Eliminar o fator comum:

2

= t \cdot 1

Multiplicar:

t \cdot 1 = t

= t

= - \frac{1}{2} + t - \frac{1}{2} t^{2}

= - \frac{1}{2} + t - \frac{1}{2} t^{2}

= c - \frac{1}{2} + t - \frac{1}{2} t^{2}

arctan (y) = c - \frac{1}{2} + t - \frac{1}{2} t^{2}

arctan (y) = c - \frac{1}{2} + t - \frac{1}{2} t^{2}

arctan (y) = c - \frac{1}{2} + t - \frac{1}{2} t^{2}

Aplique as propriedades trigonométricas inversas

arctan (y) = c - \frac{1}{2} + t - \frac{1}{2} t^{2}

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

y = tan (c - \frac{1}{2} + t - \frac{1}{2} t^{2})

y = tan (c - \frac{1}{2} + t - \frac{1}{2} t^{2})

\frac{15 - 3}{3} = 5 - \frac{2}{3} \cdot csc (4 x + \frac{π}{2})

tan (x) + 4 sin (x) = 0

1 + 2 \cdot sin (x) = 2

1 + 2 \cdot sin (x) = 3

sin (α) = \frac{120 sin ( 6 0 ^{\circ} )}{1200}