8400=624sin((2pi)/(365)t)+8736

Solución

8400 = 624 sin (\frac{2 π}{365} t) + 8736

t = - \frac{365 \cdot 0.56861 \dots}{2 π} + 365 n, t = \frac{365}{2} + \frac{365 \cdot 0.56861 \dots}{2 π} + 365 n

Pasos de solución

8400 = 624 sin (\frac{2 π}{365} t) + 8736

Intercambiar lados

624 sin (\frac{2 π}{365} t) + 8736 = 8400

Mover

8736

al lado derecho

624 sin (\frac{2 π}{365} t) = - 336

Dividir ambos lados entre

624

sin (\frac{2 π}{365} t) = - \frac{7}{13}

Aplicar propiedades trigonométricas inversas

\frac{2 π}{365} t = arcsin (- \frac{7}{13}) + 2 πn, \frac{2 π}{365} t = π + arcsin (\frac{7}{13}) + 2 πn

Resolver

\frac{2 π}{365} t = arcsin (- \frac{7}{13}) + 2 πn : t = - \frac{365 arcsin ( \frac{7}{13} )}{2 π} + 365 n

Resolver

\frac{2 π}{365} t = π + arcsin (\frac{7}{13}) + 2 πn : t = \frac{365}{2} + \frac{365 arcsin ( \frac{7}{13} )}{2 π} + 365 n

t = - \frac{365 arcsin ( \frac{7}{13} )}{2 π} + 365 n, t = \frac{365}{2} + \frac{365 arcsin ( \frac{7}{13} )}{2 π} + 365 n

Mostrar soluciones en forma decimal

t = - \frac{365 \cdot 0.56861 \dots}{2 π} + 365 n, t = \frac{365}{2} + \frac{365 \cdot 0.56861 \dots}{2 π} + 365 n

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