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

Solution

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

Solution steps

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

Switch sides

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

Move

8736

to the right side

624 sin (\frac{2 π}{365} t) = - 336

Divide both sides by

624

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

Apply trig inverse properties

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

Solve

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

Solve

\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

Show solutions in decimal form

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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