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Chapter 4 Trigonometric Functions
4.6
MATHPOWERTM 12, WESTERN EDITION 4.6.1
The Reciprocal Functions
The graphs of y = tanq and the reciprocal trigonometric
functions are periodic functions, but they differ from the
sinusoidal functions y = sinq and y = cosq in that they have
restrictions on their domains.
Recall the reciprocal functions:
1
cscx 
sin x
1
secx 
cos x
1
tan x 
cot x
The transformations that will be applied to the reciprocal
functions follow the same rules as those of the primary ratios.
y = acsc b(x + c) + d
4.6.2
Graphing the Tangent Function
Asymptotes:
Period:
Domain:
Range:
4.6.3
Graphing the Cotangent Function
1. Draw
vertical
asymptotes.
2. Plot the
points at
y = 1 and
-1.
3. Sketch
the cotangent
function.
4.6.4
Graphing the Cotangent Function [cont’d]
Asymptotes:
Period:
Domain:
Range:
4.6.5
Graphing the Cosecant Function
1. Draw the
vertical
asymptotes.
2. Plot the
points at
y = 1 and
-1.
3. Sketch
the cosecant
function.
4.6.6
Graphing the Cosecant Function [cont’d]
Asymptotes:
Period:
Domain:
Range:
4.6.7
The Cosecant Function
y = csc x
Asymptotes:
Domain:
Range:
Period:
4.6.8
Graphing the Secant Function
1. Draw the
vertical
asymptotes.
2. Plot the
points at
y = 1 and
-1.
3. Sketch
the secant
function.
4.6.9
Graphing the Secant Function [cont’d]
Asymptotes:
Period:
Domain:
Range:
4.6.10
Suggested Questions:
Page 232
1-11 odd,
12-15 (graphing calculator),
16, 17
4.6.11