What have we learned?

The graph of y = a sin ( b ( x + c))+ d transforms the graph of y= sin x in the following way:
$a$ causes a vertical stretch, shrink and/or reflection about the x endamath-axis.
amath b causes a horizontal stretch, shrink and/or reflection about the y endamath-axis.amath
c translates the graph horizontally.
d translates the graph vertically.

The cosine function is very similar to the sine function in that it shares the same shape, amplitude and period.

Download the MATLAB GUI files, cosineplot.m and cosineplot.fig, to discover the transformation of y= cos x into y =a cos( b ( x + c ) )+ d.

Please take a short quiz to put your knowledge to the test!