Having some trouble with the phase shift of this problem.

Graph y=4-3/4sec(3x-∏)

I graphed cos first but the p.s. keeps me up at night. Any walk throughs would be appreciated!

Thanks

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- Dec 21st 2010, 08:33 AMlinipopentGraph y=4-3/4sec(3x-∏)
Having some trouble with the phase shift of this problem.

Graph y=4-3/4sec(3x-∏)

I graphed cos first but the p.s. keeps me up at night. Any walk throughs would be appreciated!

Thanks - Dec 21st 2010, 08:40 AMe^(i*pi)
Is it

I would go one step at a time. If y=f(x) then

f(3x) is f(x) compressed by a factor of 3 (in other words you'll complete 3 cycles in every 2pi radians)

f(x-pi) is f(x) shifted pi units to the right on the x axis

(3/4)f(x) is a vertical "stretch" of 3/4. For trig graphs this only really changes the extrema - in this case f(x) will vary between -3/4 and 3/4

-f(x) is f(x) inverted/flipped in the x axis

4-f(x) is f(x) shifted up the y axis by 4 units.

If you confirm the equation in question I will graph these steps for you using software - Dec 21st 2010, 12:18 PMlinipopent
Sorry for Double post check down

- Dec 21st 2010, 12:33 PMlinipopent
Its the second equation.

The equation had no parenthesis around the -3/4 (amplitude)

The trouble I am having is dividing the P.S. into four equal parts.

P.S. -d/b= ∏/3 (Start) Period 2∏/b=2∏/3 (End)

What are the points in between? - Dec 22nd 2010, 09:26 AMe^(i*pi)
Your phase shift is . Therefore if you draw the graph of (I don't know if this is correct since I still don't know if sec(x) is in the numerator or denominator but cos was mentioned in the OP)

From the graph of cos(3x) your phase shift will be units in the positive direction of the x-axis. Essentially it maps each value of to a value of (I introduced theta to make it easier to understand)

__Spoiler__:

edit: with regards to the image the phase difference should be pi/3 - Dec 22nd 2010, 11:02 AMlinipopent
Sec(x) is in the numerator

4 is the demoninator - Dec 24th 2010, 11:08 AMlinipopent
What are the x-axis values in between -2/pi to 2/pi and 2/pi to pi?