Hello everyone. I need some help with these math problems. I wasn't sure if I should put this in the Pre-Calc or Calc section (its a Calc course, but the beginning of the book).
1) Let a, b be two angles. If b=a-π, how much is sin(2a+b)?
This is what I did, I'm not sure if I'm on the right track:
sin(2a+b) ---> sin(2a+(a-π)) ---> sin2a cos(a-π) + sin (a-π) cos2a
As I said, I'm not sure if I'm on the right track. If I am on the right track, how would I simplify that, because my answer does not match any of the multiple choice.
2) Using the fact that 75=2 x 60-45, compute cos(5π/12) and write the answer in its most simplified form.
I'm not even sure where to begin here. When I make 2π = 360, I end up with cos(900/12) or cos(75) which equals 0.9217512697.
I'm totally lost here to be honest.
3) If f(x)=e^(x+1) and g(x)=x^(2)+1, what is the range of the composite function f(g(x))?
I think I might know what I'm doing here.
f(g(x)) --> f(x^(2)+1) = e^(x+1) = e^(x^(2)+1)+1
Judging by what I got there, I want to say that the range is the set of all numbers. I graphed it and got a parabola. However, please help me out if I did the calculations wrong.
Thank you very much in advance to whoever helps me out on this!