First of all, it should be obvious that your A value is negative. Why?
So, one question i'm stuck in is "Find a formula for the graph of the function y=f(x) given in the figure above." (below)
For the formula f(t) = Acos(B(t+h))+C, I figured the following out:
amplitude = 3
period = 2π (2π/B=2π, B=1)
h (horizontal shift) = π
C (vertical shift) = 4
and replaced into the formula to get:
f(t) = 3cos(1(t+π))+4
Now when I graph that on my calculator, it looks fine, but it's not the correct answer. Where did I mess up? Am I even supposed to be using cos? The only reason I did is because it seemed like calculating h (the horizontal shift) would be easier for cos than sin, but I don't see why it shouldn't work either way.
Any help is greatly appreciated.
Yep. That was it. I plugged the values into C-Acos(B(t+h)) and I got 4-3cos(x), which was correct.
Thanks a ton for the help, I didn't even realize that my graph was a flipped cosine. However, for future reference, would it have also been right to see it as having shifted left/right by π like so: 4+3cos(x+/-π) ? In class, we were told to account for the difference that way, and it seems like that would be more universally applicable.