Understanding Trig Function Behavior: Period, Amplitude, and Shifts

AI Thread Summary
The discussion focuses on analyzing the trigonometric function y=-3cos(2x-π/6)+1. The user correctly identifies the period as π, the horizontal phase shift as 15 degrees to the left, and the vertical displacement as 1 unit up. They determine the maximum value to be 4, the minimum value to be -2, the amplitude as 3, and the range as {y: -2 ≤ y ≤ 4}. Other participants confirm that the user's calculations for the period, domain, and shifts are accurate.
aisha
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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 ? :redface: 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.

CAN SOMEONE PLEASE HELP ME JUST NEED HELP WITH THE MAX AND MIN THANKS :blushing:
 
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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! :blushing:
 
what are the max and min values of the cos function?
Use that to figure out the max and min values of y.
 
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! :blushing:
yes, those are correct.
 
is everything else correct too the period domain and shifts?
 
Yes - everything else looks ok.
 

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