Question 1042541
The high tide is 2 feet above a level of 4 ft
and the low tide is 2 ft below that level of 4 ft
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That tells me the amplitude must be {{{ 2 }}}
and I have to add a constant of {{{ 4 }}}  to the cosine
function
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If the function is {{{ f(x) }}}, then I want {{{ x = 0 }}}
to {{{ x = 12 }}} to equal 1 period ( 12 hrs )
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So far the function looks like:
{{{ f(x) = 2*cos( k*x ) + 4 }}}
{{{ f(12) = 2*cos( k*12 ) + 4 }}}
{{{ k*x = 2*pi }}} ( 1 period of the cosine )
{{{ k*12 = 2*pi }}}
{{{ k = pi/6 }}}
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Now I have:
{{{ f(x) = 2*cos( (pi/6)*x )  + 4 }}}
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Here's a plot of 1 period of the function
from {{{ x = 0 }}} to {{{ x = 12 }}}
{{{ graph( 600, 300, -1, 13, -1, 6, 2*cos( ( pi/6)*x ) + 4 ) }}}