Question 1163197
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Graphically....<br>
(1) y = cos(x)<br>
{{{graph(400,200,-2pi,2pi,-2,2,cos(x))}}}<br>
(2) Translate pi/2 to the left means cos(x) becomes cos(x+pi/2)<br>
{{{graph(400,200,-2pi,2pi,-2,2,cos(x+pi/2))}}}<br>
(3) Reflect over x axis means cos(x+pi/2) becomes -cos(x+pi/2)<br>
{{{graph(400,200,-2pi,2pi,-2,2,-cos(x+pi/2))}}}<br>
The resulting graph is the graph of sin(x).<br>
Algebraically....<br>
{{{-cos(x+pi/2) = -(cos(x)cos(pi/2)-sin(x)sin(pi/2)) = -(cos(x)(0)-sin(x)(1)) = sin(x)}}}<br>