Graphing sine / cosine / tangent (and inverses) w/o a calculator help

These questions have been killing me and I have no idea how to do them, please help

y=1/2cot(2x - pi/2)

y=2csc(2x/3 - pi/3)

y=-5/2sin(3x - 3pi/2) +2

y=-3cos(x/2 + 2pi/3)-2

y=2sec(x - pi/4)

Re: Graphing sine / cosine / tangent (and inverses) w/o a calculator help

Hey Kiith.

Hint: For the first one, you should try graphing the tan function and then adjust for the scale factor (2x) and then the translation factor (-pi/2) and use the fact that cot(x) = 1/tan(x).

You can use google to see what tan(x) looks like:

tan(x) - Wolfram|Alpha

Re: Graphing sine / cosine / tangent (and inverses) w/o a calculator help

I understand that it's that I'm having trouble applying the phase shift or finding the 5 key points.

For example in the 3rd one I got pi/2 as the phase shift by setting 3x-3pi/2 to zero and

Got the period to be 2pi/3 and then divided that by 4 to get where my graph starts which is pi/6 which

sounds conpletely wrong