Question

Question on the handout for Lecture on sinusoidal wave.

Answer 1

I am confused with the step c in the proof. How did they shrink the x axis. How come it results in a equation \[\sin k \left( x+2\pi /k \right)\]

Answer 2

They are referring to item (3) in
http://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/readings/g_graphng_fnctns.pdf

which briefly explains that multiply by k "shrinks" the x-axis