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 18
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43θ
θ
52. Sketch the graph of the function y = csc
by making a table of values. Use angles
in the interval
θ
π
π
0 ≤
≤ 2
which are multiples of
12
.
Figure T35b
θ
θ
53. Sketch the graph of the function y = sec
by making a table of values. Use angles
in the
π
θ
π
π
−
≤
≤
interval
2
3
2
which are multiples of
12
.
Figure T35c
INVERSE TRIGONOMETRIC FUNCTIONS
A portion of the graph of y = sin x is
shown in Figure T36. Over the interval
π
π
−
x =
to x =
, the sine function
2
2
takes on each of its values exactly once.
Consequently, for each y between -1 and
+1 there is exactly one number x between
π
π
−
2
and
2
for which y = sin x. In this
way the portion of the graph of y = sin x
π
π
−
between x =
2
and x =
2
determines
a function which associates a unique number
π
π
−
between
and
with each number
2
2
Figure T36 y = sin x
between -1 and 1. This function is called the
inverse sine function and is denoted
- 18 -
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