Hi, could somebody clear this up.
cosx=sinpi/2-x
I must be doing something wrong, because as far as I'm aware this is
sin(-x) which should transform the sin graph by flipping it around the y axis, followed by sin((-x)+pi/2) which should shift the graph backward by pi/2. However this graph looks like cosx flipped around the x axis..?
Alternatively I call this sin-(x-pi/2), so that's sin((x)-pi/2) which shifts the graph to the right by 1/4 of a period, then sin-((x)-pi/2) which flips it around the y axis, although by this time the graph is symmetrical about the axis anyway and so, again, I end up with cos(-x), cosx flipped around the x axis.
So in conclusion by transforming I'm finding that -cosx=sinpi/2-x, which is wrong. What's up?
Thanks.
Well if you want to map a function f(x) to f(ax+b), then translating it first and then compressing gives different result from doing it the other way round.
The right way is to translate first then, compress.
In your case translate by then flip, you will get what you want.
What you have done is wrong because when you first flipped it and then translated it by , you have essential translated in the flipped axis. In other words, from the original axis point of view, you have translated the graph by in the opposite direction. That is to say, you flipped, thus that gave -x, then you translated by , which is actually a in the original axis.Thus it gave you
Hmm... why do you do the translation first?
From how I understand functions, say we have
sin(x)
Then we translate to the left by pi/2 to get
sin(x+pi/2)
Which looks like the cosine graph.
Now say u=x+pi/2
So the function is currently sinu
Then we do the flip around the axis as you say, giving
sin-u
Which is
sin-(x+pi/2)
Which is
sin(-x-pi/2)?
Which is incorrect...
I don't understand why you can't say u=x-pi/2 and then the function =sin-u=sin(pi/2-x) which would achieved by translating right then flipping?
I'm confused.
Hey, you are flipping the wrong way. Replacing x by -x is flipping about y axis.
The problem is you are seeing sin(-x) = -sin x and thinking about flipping the curve about x-axis. You should not do this. In the procedure explained, when you translate by pi/2, you no longer have a curve that looks like sin(In fact it is cos). Thus "sin(-x) = -sin x" will not hold.