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Popular >

d^2+13d+36=(sin^2(x))/2

Solución

d^{2} + 13 d + 36 = \frac{sin ^{2} ( x )}{2}

Solución

x = arcsin (2 d^{2} + 26 d + 72) + 2 πn, x = π + arcsin (- 2 d^{2} + 26 d + 72) + 2 πn, x = arcsin (- 2 d^{2} + 26 d + 72) + 2 πn, x = π + arcsin (2 d^{2} + 26 d + 72) + 2 πn

Pasos de solución

d^{2} + 13 d + 36 = \frac{sin ^{2} ( x )}{2}

Intercambiar lados

\frac{sin ^{2} ( x )}{2} = d^{2} + 13 d + 36

Usando el método de sustitución

\frac{sin ^{2} ( x )}{2} = d^{2} + 13 d + 36

Sea:

sin (x) = u

\frac{u ^{2}}{2} = d^{2} + 13 d + 36

\frac{u ^{2}}{2} = d^{2} + 13 d + 36 : u = 2 d^{2} + 26 d + 72, u = - 2 d^{2} + 26 d + 72

\frac{u ^{2}}{2} = d^{2} + 13 d + 36

Multiplicar ambos lados por

2

\frac{u ^{2}}{2} = d^{2} + 13 d + 36

Multiplicar ambos lados por

2

\frac{2 u ^{2}}{2} = 2 d^{2} + 2 \cdot 13 d + 2 \cdot 36

Simplificar

u^{2} = 2 d^{2} + 26 d + 72

u^{2} = 2 d^{2} + 26 d + 72

Para

x^{2} = f (a)

las soluciones son

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

u = 2 d^{2} + 26 d + 72, u = - 2 d^{2} + 26 d + 72

Sustituir en la ecuación

u = sin (x)

sin (x) = 2 d^{2} + 26 d + 72, sin (x) = - 2 d^{2} + 26 d + 72

sin (x) = 2 d^{2} + 26 d + 72, sin (x) = - 2 d^{2} + 26 d + 72

sin (x) = 2 d^{2} + 26 d + 72 : x = arcsin (2 d^{2} + 26 d + 72) + 2 πn, x = π + arcsin (- 2 d^{2} + 26 d + 72) + 2 πn

sin (x) = 2 d^{2} + 26 d + 72

Aplicar propiedades trigonométricas inversas

sin (x) = 2 d^{2} + 26 d + 72

Soluciones generales para

sin (x) = 2 d^{2} + 26 d + 72

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (2 d^{2} + 26 d + 72) + 2 πn, x = π + arcsin (- 2 d^{2} + 26 d + 72) + 2 πn

x = arcsin (2 d^{2} + 26 d + 72) + 2 πn, x = π + arcsin (- 2 d^{2} + 26 d + 72) + 2 πn

sin (x) = - 2 d^{2} + 26 d + 72 : x = arcsin (- 2 d^{2} + 26 d + 72) + 2 πn, x = π + arcsin (2 d^{2} + 26 d + 72) + 2 πn

sin (x) = - 2 d^{2} + 26 d + 72

Aplicar propiedades trigonométricas inversas

sin (x) = - 2 d^{2} + 26 d + 72

Soluciones generales para

sin (x) = - 2 d^{2} + 26 d + 72

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- 2 d^{2} + 26 d + 72) + 2 πn, x = π + arcsin (2 d^{2} + 26 d + 72) + 2 πn

x = arcsin (- 2 d^{2} + 26 d + 72) + 2 πn, x = π + arcsin (2 d^{2} + 26 d + 72) + 2 πn

Combinar toda las soluciones

x = arcsin (2 d^{2} + 26 d + 72) + 2 πn, x = π + arcsin (- 2 d^{2} + 26 d + 72) + 2 πn, x = arcsin (- 2 d^{2} + 26 d + 72) + 2 πn, x = π + arcsin (2 d^{2} + 26 d + 72) + 2 πn

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sin^2(x)-cos^2(x)=cos^4(x)

sin^{2} (x) - cos^{2} (x) = cos^{4} (x)