Question 1140710
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(1) minimum at (0,3) means either a negative cosine function with no horizontal shift or a shifted sine function; since the shift makes the equation more complicated, we will use a negative cosine function.<br>
{{{f(x) = -a*cos(bx)+d}}}<br>
(2) An amplitude of 6 and a minimum at (0,3) means the center line is 3+6 = 9.<br>
{{{f(x) = -6*cos(bx)+9}}}<br>
(3) The period is 45 degrees (pi/4 radians), which is 1/8 of the period of the basic cosine function:<br>
{{{f(x) = -6*cos(8x)+9}}}<br>
A graph: center line 9; minimum 3 and maximum 15; period pi/4 = 0.785 approximately....<br>
{{{graph(1200,200,-pi/2,3pi/2,-3,21,-6*cos(8x)+9)}}}