Sketching a graph of secx on an interval

Question

When making a graph for secx on interval [ (-pi/(2) , (3pi)/(2) ] how do I know the numbers in between these two to put on the x axis?

Answer 1

Alex,

 

Can you graph cosX on this interval?

 

COSX = 0 for: - π/2, π/2, (3/2)π

 

COSX = 1 for X = 0

 

          = -1 for X = π

 

secx = 1 / COSX

 

Therefor: on your graph of secx: 

 

1. you will have vertical asymptotes at X = - π/2, Π/2, and (3/2)π

 

2. you will also have the following points:  (0,1), (π,-1)

 

3. from the point (0,1) the curve will go up to the left and up 

    to the right, never crossing the vertical asymptotes

 

4. from the point (π,-1) the curve will go down to the left and 

    down to the right, never crossing either vertical asymptote

 

Remember:   -1 ≥ secx  and secx ≥ 1