Similar Triangles, Right Triangles, And The Definition Of The Sine, Cosine And Tangent Functions Of Angles Of A Right Triangle Worksheets With Answer Key Page 17
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43θ
θ
Figure T33 Graph of y = sec
Figure T34 Graph of y = csc
θ
θ
sec =
The cosine function is also plotted so that you can see the reciprocal relationship
1
cos
π
between these functions. Both the secant and cosecant have period 2
. For instance, one complete
θ
π
θ
π
−
=
section of the graph of the secant lies between
=
2
and
3
2
. The secant function has
π
vertical asymptotes at odd multiples of
2
(where the cosine function is 0).
π
The graph of the cosecant function is shown in Figure T34. It is just the secant graph displaced
2
units to the right. You should be able to construct the graphs of the secant and cosecant functions.
Problems:
θ
θ
45. The period of y = csc
is
.
46. The period of y = tan
is
.
θ
θ
47. The period of y = cos
is
.
48. The period of y = cot
is
.
θ
θ
49. The period of y = sin
is
.
50. The period of y = sec
is
.
θ
θ
51. Sketch the graph of the function y = cot
by making a table of values. Use angles
in the
θ
π
π
interval 0 ≤
≤
which are multiples of
12
.
Figure T35a
- 17 -
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