Question 420241: How do I graph y=2+3cos(3x-pi/4)? Thanks for your help!
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! How do I graph y=2+3cos(3x-pi/4)? Thanks for your help!
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y=2+3cos(3x-pi/4)
Wish I could draw a diagram for you but,I will have to do it with words.
By inspection of the given expression, the amplitude=3, and the curve will be bumped up 2 units.
Period = 2pi/B=2pi/3=(2/3)pi or (B=the coefficient of x)
Phase Shift:
set 3x-pi/4=0
then solve for x
3x=pi/4
x=pi/12=(1/12)pi=phase shift
Divide period into four intervals
2pi/3*1/4=pi/6
1/4 period=(1/6)pi or (2/12)pi
drawing the graph for one period:
On the x-axis, mark point (1/12)pi (this is where the cos graph starts)
mark the second point on the x-axis which will be (3/12)pi (we added a quarter point to the starting point. Add a quarter point for the third point, (5/12)pi.
The fourth and 5th points will then be (7/12)pi and (9/12) pi. Note that from the first point, (1/12)pi to the fifth point (9/12) we covered one period=(8/12)pi. We can now draw the cos curve.The ordered pairs will be:
(pi/12,5),(pi/4,0),(5pi/12,-1,),(7pi/12,0), and (9pi/12,5).
The graph below will give you some idea what we did: Remember, the cos function goes on forever, but we did it for only one period.
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