This question is related to standing waves from physics, but mostly contains math.
Let,
$y_1 = A \cos {( \alpha t + k )}$
$y_2 = A \cos (\beta t + c )$ where $k,c$ are arbitrary, real constants.
How would you sketch $y_3=y_1+y_2$?
Using the appropriate trigonometric identity, we can simplify this to -
$y_3 = 2A \cos \bigg( \dfrac {(αt + k)+(βt + c)} { 2}\bigg ) \cos \bigg( \dfrac {(αt + k)-(βt + c)} { 2} \bigg)$
But, I don't know how to proceed from there.
Thanks in advance.