Mathematics, 30.01.2020 00:52 haimar8710
Waves with an amplitude of 2ft pass a doc every 30 seconds. write an equation for a cosine model the height of a water particle above and below the mean water line
Answers: 2
![\bf ~~~~~~~~~~~~\textit{function transformations} \\\\\\ f(x)=Asin(Bx+C)+D \qquad \qquad f(x)=Acos(Bx+C)+D \\\\ f(x)=Atan(Bx+C)+D \qquad \qquad f(x)=Asec(Bx+C)+D \\\\[-0.35em] ~\dotfill\\\\ \bullet \textit{ stretches or shrinks}\\ ~~~~~~\textit{horizontally by amplitude } A\cdot B\\\\ \bullet \textit{ flips it upside-down if }A\textit{ is negative}](/tpl/images/0483/9141/fde18.png)
![\bf \stackrel{\textit{horizontal shift of }\frac{15}{2}}{\cfrac{15}{2}=\cfrac{C}{B}}\implies \cfrac{15}{2}=\cfrac{C}{~~\frac{\pi }{15}~~}\implies \cfrac{15}{2}=\cfrac{15C}{\pi }\implies 15\pi =30C \\\\\\ \cfrac{15\pi }{30}=C\implies \cfrac{\pi }{2}=C~\hfill \stackrel{\textit{horizontally to the right}}{-\cfrac{\pi }{2}=C} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill g(x)=2cos\left(\frac{\pi }{15}x-\frac{\pi }{2} \right)~\hfill](/tpl/images/0483/9141/506f6.png)
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