What is the general solution for 900=400sin((2pit}{365}+\frac{7pi)/8)+500 ?

The general solution for 900=400sin((2pit}{365}+\frac{7pi)/8)+500 is t=365n-1095/16

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900=400sin((2pit}{365}+\frac{7pi)/8)+500

900 = 400 sin (\frac{2 π t}{365} + \frac{7 π}{8}) + 500

t = 365 n - \frac{1095}{16}

Solution steps

900 = 400 sin (\frac{2 π t}{365} + \frac{7 π}{8}) + 500

Switch sides

400 sin (\frac{2 π t}{365} + \frac{7 π}{8}) + 500 = 900

Move

500

to the right side

400 sin (\frac{2 π t}{365} + \frac{7 π}{8}) = 400

Divide both sides by

400

sin (\frac{2 π t}{365} + \frac{7 π}{8}) = 1

General solutions for

sin (\frac{2 π t}{365} + \frac{7 π}{8}) = 1

\frac{2 π t}{365} + \frac{7 π}{8} = \frac{π}{2} + 2 πn

Solve

\frac{2 π t}{365} + \frac{7 π}{8} = \frac{π}{2} + 2 πn : t = 365 n - \frac{1095}{16}

t = 365 n - \frac{1095}{16}

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What is the general solution for 900=400sin((2pit}{365}+\frac{7pi)/8)+500 ?
The general solution for 900=400sin((2pit}{365}+\frac{7pi)/8)+500 is t=365n-1095/16