# Transformation of sinusoids

We want to get $h(x)= 0.29\cos(3x+4.2)$

$y = \cos x$ -> multiply $x$-axis 0,29 -> $y=0.29\cos x$ -> multiply $y$-axis $1/3$ -> $y=0.29\cos(3x)$ -> translation $(-1,4;0)$ -> $h(x) = 0.29\cos(3x+4.2)$

Is this correct? I know you can more easily translate first, however I like to use as a rule of thumb to always multiply before translating.

-
The $0.29$ has the effect of shrinking in the vertical ($y$-axis) direction. The reason for that should become apparent if you think about plotting points. Similarly, the $3$ shrinks in the $x$-direction.