# Trig functions behaviour

1. Aug 30, 2005

### 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 wont give me the values for max and min. Therefore I cannot solve for amplitude yet and same with range.

2. Aug 30, 2005

### 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!

3. Aug 30, 2005

### Fermat

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

4. Aug 30, 2005

### Fermat

yes, those are correct.

5. Aug 30, 2005

### aisha

is everything else correct too the period domain and shifts?

6. Aug 30, 2005

### Fermat

Yes - everything else looks ok.