4.6 Graphs of Other Trigonometric Functions
y = csc x
Use the values of the unit circle to graph y = csc x . Keep in mind that csc x =
1
.
sin x
y = sec x
Use the values of the unit circle to graph y = sec x . Keep in mind that sec x =
1
.
cos x
In the formula: y = A sec (Bx - C) and y = A csc (Bx - C)
Amplitude = undefined
Period =
2π
B
Phase Shift =
C
B
1
Example 1: y = sec (2 x + π )
2
⎛x π⎞
Example 2: y = 2 csc ⎜ − ⎟
⎝ 2 4⎠
−
3π
3π
<x<
4
4
y = tan x
Use the values of the unit circle to graph y = tan x . Keep in mind that tan x =
sin x
.
cos x
y = cot x
Use the values of the unit circle to graph y = cot x . Keep in mind that cot x =
cos x
.
sin x
Graphing tan x, cot x, csc x and sec x
with shifts in the amplitude, period and phase shift
In the formula: y = k + A tan (Bx - C) and y = A cot (Bx - C) + k
Amplitude = undefined. (graph has no max or min. point)
| A | > 1 steeper graph
| A | < 1 flatter graph
When A is negative the graph is reflected over x-axis.
Period =
π
B
Phase Shift =
C
B
Example 3: Graph the following function by hand and check in the graphing calculator.
⎛x⎞
y = 2 cot ⎜ ⎟ − 2π < x < 2π
⎝2⎠
Hint: Type in calculator as 2 / tan (x/2)
Example 4: Graph the following function by hand and check in the graphing calculator.
π⎞
⎛
y = tan ⎜ 2 x + ⎟
4⎠
⎝