1. Graph of Cosecant

I need help with sketching this graph:
y=2csc(-x-Pi/2)+1
(The -x in the equation is what's throwing me off...)

This is what I know so far:
Altitude:2
Period:-2pi
Phase Shift: Pi/2 (to the right)
Vertical Shift: 1 (up)

The x-axis needs to be in radians. So I believe the tick marks on the x-axis should be (from left to right) -2pi, -3pi/2 -pi, -pi/2, pi/2, pi, 3pi/2, and 2pi

2. Re: Graph of Cosecant

Hey jls9102.

Recall that f(-x) takes f(x) and reflects around the y-axis and that f(x-a) shifts the graph a units to the right along the x-axis where a*f(x) stretchs it (and possibly flips it) and finally f(x) + a shifts everything a units up in the direction of the y-axis.

So consider f(x + pi/2) first and then reflect that on the y-axis and take it from there.

3. Re: Graph of Cosecant

Ok so ultimately will the equation look like this:
y=-2csc(x+Pi/2)+1

Or would it change to:
y=-2csc(x+Pi/2)-1