I'm currently brushing up my trig and found these two problems. I'm totally clueless on how to start. Please help.
Find the period , amplitude , and phase angle, and use these to sketch
a) $$3\sin(2x − π)$$
b) $$−4\cos(x + π/2)$$
In simple words. When talking about a periodic function:
Whereas the period has a strict absolute definition, the amplitude and the phase are subject for the convention. There is however a strict definition for relative amplitude and phase.
Now, about your exercise.
If you have a function of the form f(x) = |a| sin (bx + c) then:
Note: we actually defined a convention here. The amplitude is the maximum value of the function, and the phase=0 is defined for the point where the function is 0 with positive derivative.
f(x) = 3sin(2x−π) = 3sin(2x+π)
f(x) = −4cos(x+π/2) = 4sin(x) [trigonometry equality]