What is expand 3sin((2pi)/(365)(t-79))+12 ?

The solution to expand 3sin((2pi)/(365)(t-79))+12 is 3sin((2pit-158pi)/(365))+12

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expand 3sin((2pi)/(365)(t-79))+12

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3 sin (\frac{2 π}{365} (t - 79)) + 12

3 sin (\frac{2 π t - 158 π}{365}) + 12

Solution steps

3 sin (\frac{2 π}{365} (t - 79)) + 12

3 sin (\frac{2 π}{365} (t - 79)) = 3 (cos (\frac{158 π}{365}) sin (\frac{2 π t}{365}) - sin (\frac{158 π}{365}) cos (\frac{2 π t}{365}))

= 3 (cos (\frac{158 π}{365}) sin (\frac{2 π t}{365}) - sin (\frac{158 π}{365}) cos (\frac{2 π t}{365})) + 12

Use the Angle Difference identity:

sin (s) cos (t) - cos (s) sin (t) = sin (s - t)

= 3 sin (\frac{2 π t}{365} - \frac{158 π}{365}) + 12

Join

\frac{2 π t}{365} - \frac{158 π}{365} : \frac{2 π t - 158 π}{365}

= 3 sin (\frac{2 π t - 158 π}{365}) + 12

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What is expand 3sin((2pi)/(365)(t-79))+12 ?
The solution to expand 3sin((2pi)/(365)(t-79))+12 is 3sin((2pit-158pi)/(365))+12