Question

For f(x) = 1/2sin2(x-90°)

What are the transformations?

The 1/2 means a vertical compression by a factor of 1/2

And (x-90°) means there's a phase shift right 90°

But what does the 2 mean? The one immediately left to the (x-90°).

Does it mean a horizontal compression by factor of 1/2?

Because when I draw the graph for it going by what I have above, I get something different from what I calculate the main 5 points as :

(x,y) -> (2x+90°, 1/2y)
(0,0) -> (90°, 0)
(90,1)-> (270, 1/2) ... When I draw the graph, the point I get is (270, 0).

Answer 1

The 2 in
f(x) = (1/2) sin 2(x-90°) affects the frequency

for sin k(....), the period of the sine curve is 360°/k
or we can say that there are k complete curves from 0 to 360
So the 2 causes a compression factor of 2 of the standard sine curve.
that is, for f(x) = (1/2) sin (x-90°) there would be ONE complete sine curve from 0 to 360 , while for
f(x) = (1/2) sin 2(x-90°) there will be TWO complete sine curves from 0 to 360

So, let's say we pick x = 30·
we have
f(30°) = (1/2) sin 2(30-90°)
= (1/2) sin 2(-60°)
= (1/2) sin (-120°)
= (1/2)(-√3/2) = -√3/4 or appr -.433

etc