You did a mistake there - you misuse the trigonometric identity. Look at http://www.sosmath.com/trig/Trig5/trig5/trig5.html It's 2⋅cos(x)⋅sin(x)=sin(2x)2⋅cos(x)⋅sin(x)=sin(2x) Not cos(x)⋅sin(x)=sin(s)cos(x)⋅sin(x)=sin(s) Sha...
If you look at the their graphs (http://study.com/academy/lesson/graphing-sin-cosine-transformations.html) you will see that they are the same wave function but are out of phase. In other words, one is shifted over to the left. Using the right triangle definitions, sine is th...