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Home » Time for first part: \( \frac30060 = 5 \) hours. - Veritas Home Health

Time for first part: \( \frac30060 = 5 \) hours. - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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h(t) = 4\sin\left(\frac{\pi}{6}t\right) + 3\cos\left(\frac{\pi}{6}t\ri...
This can be expressed as:
h(t) = R\sin\left(\frac{\pi}{6}t + \phi\right)
where $ R = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5 $
So the maximum height is $ \boxed{5} $.
To find the time at which this maximum occurs, we use:
\tan\phi = \frac{3}{4} \Rightarrow \phi = \arctan\left(\frac{3}{4}\rig...
The maximum of $ \sin(\cdot) $ occurs when its argument is $ \frac{\pi...
\frac{\pi}{6}t + \phi = \frac{\pi}{2} \Rightarrow t = \frac{\frac{\pi}...
Using $ \arctan\left(\frac{3}{4}\right) \approx 0.6435 $ radians:

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