# Trig functions behaviour

aisha
Hi just need a little help with the behaviour of this trig function

$$y=-3\cos (2x-\frac {\pi} {6}) +1$$
I converted the pi over 6 to degrees and got -30

need to state the period, amplitude, max/min values, range, domain, horizontal phase shift, and vertical dispacement.

So far after rearranging the the equation i have

period= $$pi$$
range= ?
amplitude=?
domain= all values XER
horizontal phase shift= 15 degrees left
vertical displacement= up 1
max\min ? not sure how to figure this out from the equation i tried graphing using the graphing calculator but it won't give me the values for max and min. Therefore I cannot solve for amplitude yet and same with range.

aisha
I got
max = 4, min = -2
amplitude = 3
range = {y:-2 <= y <= 4}

is this correct or have i done something wrong..please check and reply soon!

Homework Helper
what are the max and min values of the cos function?
Use that to figure out the max and min values of y.

Homework Helper
aisha said:
I got
max = 4, min = -2
amplitude = 3
range = {y:-2 <= y <= 4}

is this correct or have i done something wrong..please check and reply soon!
yes, those are correct.

aisha
is everything else correct too the period domain and shifts?

Homework Helper
Yes - everything else looks ok.