Trigonometry Worksheet Page 15
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22DEFINITION
#
BM
H? IG?
• The secant of , written sec , is the reciprocal of cos . That is, sec =
=
.
= G
>D =? H
#
BM
H? IG?
• The cosecant of , written csc , is the reciprocal of sin . That is, csc =
=
.
GC
GCH?
#
= G
• The cotangent of , written cot , is the reciprocal of tan . That is, cot =
=
=
H
GC
>D =? H
.
GCH?
The physical interpretations (as lengths) of all six trigonometric functions can be seen on one diagram,
as shown below.
&
Example: Suppose sin =
and that
is in Quadrant 1. Determine the remaining five trigonometric
function values of
in exact (non-decimal) form.
&
Solution: In Quadrant 1, all six trigonometric functions are positive. Since sin =
, we know the
opposite leg has length 4 and hypotenuse has length 7. The Pythagorean Formula is used to determine
the length of the remaining (adjacent) leg:
{ I {
+ 4
= 7
$
$
$
{ I {
+ 16 = 49
$
{ I {
= 33
$
I
= 33
>D =? H
%%
GCH?
Since cos =
, we conclude that cos =
. Also, since tan =
, we conclude that
BM
H? IG?
>D =? H
&
& %%
tan =
=
, where the denominator was rationalized in the last step. The remaining
%%
%%
trigonometric function values are determined by taking appropriate reciprocals:
#
#
csc =
=
=
;
GC
&
&
#
#
%%
sec =
=
=
Rationalize the denominator
= G
%%
%%
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education