5.5 Graphs of Other Trig Functions Name: _______________
Objectives: Students will be able to generate the graphs for tangent, cotangent,
secant, and cosecant functions and explore various transformations of these graphs.
Graph f(x) = tanx over [-2π,2π] by [-2,2]. Use xscl: π/4 and yscl: 1
x
f(x)
-2π
-7π/4
-3π/2
-5π/4
-π
-3π/4
-π/2
-π/4
0
π/4
π/2
3π/4
π
5π/4
3π/2
7π/4
2π
Period:
Domain:
V.A.
Range:
Nov 7­10:41 AM
Examples 1.) Graph two periods of y = tan(x-π/4).
Transformations:
Period:
V.A.
Domain:
Range:
2.) Graph two periods of y = 3tan(x/2) + 1.
Transformations:
Period:
V.A.
Domain:
Range:
Nov 7­10:54 AM
1
Graph f(x) = cotx = cosx/sinx over [-2π,2π] by [-2,2]. Use xscl: π/4 and yscl: 1
x
f(x)
-2π
-7π/4
-3π/2
-5π/4
-π
-3π/4
-π/2
-π/4
0
π/4
π/2
3π/4
π
5π/4
3π/2
7π/4
Period:
2π
V.A.
Range:
Domain:
Nov 7­10:41 AM
Examples 1.) Graph two periods of y = -cot(3x).
Transformations:
Period:
V.A.
Domain:
Range:
2.) Graph two periods of y = 3cot(2x - π) - 1.
Transformations:
Period:
V.A.
Domain:
Range:
Nov 7­10:54 AM
2
Graph y1 = sinx and y2 = 1/sinx over [-2π,2π] by [-2,2].
Use xscl: π/4 and yscl: 1. What do you notice?
Domain:
Range:
Graph y1 = cosx and y2 = 1/cosx over [-2π,2π] by [-2,2].
Use xscl: π/4 and yscl: 1. What do you notice?
Domain:
Range:
Nov 7­11:01 AM
Examples 1.) Graph two periods of y = csc(2x) + 2.
Transformations:
Period:
V.A.
Domain:
Range:
Nov 7­10:54 AM
3
2.) Graph two periods of y = 3sec4(x-π/4) - 2.
Transformations:
Period:
V.A.
Domain:
Range:
Jan 22­8:04 PM
Assignment: Pages 545-546: 9, 17, 19, 21, 23, 29, 41, 45
Jan 22­8:10 PM
4
Jan 22­8:18 PM
Jan 22­8:18 PM
5