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 14
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43Problems:
π
π
2
2
35. Evaluate csc
30° - cot
30°
36. Evaluate
2
cos
sin
.
3
4
π
π
°
2
tan
45
+
2
2
37. Evaluate
38. Evaluate
sec
tan
.
.
−
°
2
3
3
2
sec
45
π
−
2
cot
1
3
39. Which of the following is the exact numerical value of
?
π
2
cot
3
3 −
3 −
−
3
3
3
1
3
A)
B)
C)
D)
E)
2
6
3
2
3
GRAPHS OF THE SINE AND COSINE FUNCTIONS
θ
θ
The graph of the function y = sin
is shown in Figure T25. The horizontal (or
) axis is in radians,
π
π
π
so the graph crosses the horizontal axis at 0, ±
, ±2
, ±3
, etc. The maximum value of the sine
π
π
π
function is 1, which occurs at
2
and
2
± 2n
for each integer n. The minimum value of the sine
θ
θ
π
function is -1. The section of the graph from
= 0 to
= 2
is one complete cycle, i.e., the graph
π
π
π
π
π
π
π
repeats itself from 2
to 4
, from 4
to 6
, etc. Similarly, it repeats from -2
to 0, from -4
to -2
,
etc.
Figure T25 The sine function
π
The graph of the cosine function is shown in Figure T26. It, too, repeats in cycles of 2
and has values
π
between -1 and 1. If the cosine graph is displaced
2
units to the right, it coincides with sine graph,
θ
π
θ
π
i.e., cos(
-
2
) = sin
. Thus, both sine and cosine complete their cycle in 2
units.
Figure T26 The cosine function
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