Transformation of trigonometry functions

[chwala]

Homework Statement

let ##f(x)= (\sin 2x + \cos 2x)^2## and ## g(x)= cos 2x-1## The graph of ##y=g(x)## can be obtained from the graph of ##y=f(x)## under a horizontal stretch of scale factor ##k## followed by a translation of vector ##(p,q)##, find the exact values of ##k, p, q##

Relevant Equations

horizontal and vertical stretch....

kindly note that this solution is NOT my original working. The problem was solved by my colleague. I have doubts with the ##k## value found. Is it not supposed to be ##k=0.5?## as opposed to ##k=2?##. From my reading on scaling, the graph shrinks when ##k## is greater than ##1## and conversely.

 

[BvU]

Homework Statement:: let ##f(x)= (sin 2x + cos 2x)^2## and ## g(x)= cos 2x-1## The graph of ##y=g(x)## can be obtained from the graph of ##y=f(x)## under a horizontal stretch of scale factor ##k## find the exact values of ##k, p, q##

You also want to tell us what ##p## and ##q## are !

##\LaTeX## tip: use \sin and \cos

 

[chwala]

You also want to tell us what ##p## and ##q## are !

##\LaTeX## tip: use \sin and \cos

sorry, i just amended the question...

 

[Doc Al]

From my reading on scaling, the graph shrinks when ##k## is greater than ##1## and conversely.

That's certainly true, but check it for yourself: Plot ##sin (x)## vs ## sin (2x)##.

 

[Mark44]

the graph shrinks when k is greater than 1 and conversely.

A better way to say this, regarding f(kx) vs. f(x) is this:
Horizontal compressions/expansions
If k > 1, the graph of y = f(kx) is the compression of the graph of y = f(x) toward the vertical axis.
If 0 < k < 1, the graph of y = f(kx) is the expansion of the graph of y = f(x) away the vertical axis.

Vertical compressions/expansions
If k > 1, the graph of y = k* f(x) is the expansion of the graph of y = f(x) away from the horizontal axis.
If 0 < k < 1, the graph of y = k* f(x) is the compression of the graph of y = f(x) toward the horizontal axis.

For negative values of k, there are reflections happening, which is a different matter.