Question 1141502
a) Determine the equation of a sine function 
<pre>
{{{y=Asin(Bx+C)+D}}}
</pre>
that would have a range of {y ER|-4≤y≤1}<pre> 
I don't understand "ER", so I'll assume the range is{y|-4≤y≤1}

The range is from -4 to 1, a span of 1-(-4)=1+4=5 units. So we know it is a
downward shifted sine function that has an amplitude of half of 5 which is
5/2, so A = 5/2.  Also, it must be shifted downward so that the horizontal
axis of symmetry is shifted from the x-axis down to halfway between -4 an 1,
which is {{{(-4+1)/2=-3/2}}}, so {{{D = -3/2}}}. So we have:

{{{y=expr(5/2)sin(Bx+C)-3/2}}}

and a period of 45 degrees.

The period is given by {{{(360^o)/B}}} so {{{360^o/B=45^"o"}}}

{{{B*45^"o"=360^o}}}

{{{B=360^o/45^o}}}

{{{B=8}}}, so we have:

{{{y=expr(5/2)sin(8x+C)-3/2}}}

and we may as well take C=0 since there is no need for any horizontal shift.

So an answer is:

{{{y=expr(5/2)sin(8x)-3/2}}}

The graph one one period (from 0° to 45° is:

{{{graph(2*800,4*800/13,-.5,45.1,-5,2,((5/2)sin(8x*(pi/180))-3/2)*sqrt(x)/sqrt(x),10,11,12,-4,1)}}}

</pre>b) Determine the cosine function that results in the same graph as the function in part (a).<pre>

Use the identity {{{sin(theta)=cos(theta-90^o)}}}

{{{y=expr(5/2)cos(8x-90^o)-3/2}}}

Edwin</pre>