4.3 - Graphs of the Other Circular Functions
Graphs of the Secant and Cosecant Functions
Amplitude = none
Period = 2π
To graph:
1 . Use y = sin x as a guide for y = csc x, and use
y = cos x as a guide for y = sec x
2. Draw vertical asymptotes at the x-intercepts
(prior to graphing the vertical translation)
3. Sketch csc x/sec x as U-shaped curves
that touch the sin x/cos x curve at max/min
points and approach the asymptotes
Graph y = csc x
amplitude _______
period_______
phase
shift_______
vertical
translation______
Graph y = sec x
amplitude _______
period_______
phase
shift_______
vertical
translation______
Function: y = csc (x - π )
3
amplitude _______
period_______
phase
shift_______
vertical
translation______
Graph y = sec (2x + π
)
3
amplitude _______
period_______
phase
shift_______
vertical
translation______
Graph y = -2 sec (3x - π)
Graph y = -2 -
1
csc
2
(2x - 3π)