91Ó°ÊÓ

Derive each equation, where \(a\) and \(b\) are constants with \(a \neq 0 .\) \(\sin (a x+b) d x=-\frac{1}{a} \cos (a x+b)+C\)

The depth of water at my favorite surfing spot varies from 5 to 15 feet, depending on the time. Last Sunday high tide occurred at \(5: 00 \mathrm{AM}\) and the next high tide occurred at 6:30 PM. a. Obtain a cosine model describing the depth of water as a function of time \(t\) in hours since 5:00 AM on Sunday morning. b. How fast was the tide rising (or falling) at noon on Sunday?

What can you say about the definite integral of a sine or cosine function over a whole number of periods?

By referring to the graph of \(f(x)=\cos x\), explain why \(f^{\prime}(x)=-\sin x\), rather than \(\sin x\).