Section 5.1
The lnteractive CD-ROM and /nternet versions of this text contain step-by-step solutions
to all odd-numbered exercises.They also provide Tutorial Exercises for additional help.
Exercises
1 -1 4, use the given values to evaluate (if possitrigonometric functions.
remaining
the
ble)
ln Exercises
l.sinx: "3
2,cos-x:
J1
J1
3
7.secd:-. cscd:
.13
t2
ln \
8.cosl--xl:-.
\,I{
/
1
J
3
4
J
=
)
J'
undefined, sin g >
4
1
15. sec x cos x
17. sslz x
csc2 x
In. Exercises
wrth one
of
(a)
(d)
(f) sin x
tan
r
csc
"x
(i - cos2x)(cscx)
stnl(r/2\ - xl
20._#
coslQrl2) - x)
21-26, match the trigonometric expression
the following.
cscx
sinxtanx
21' sinx
(c) cot x
13.
-
secx
23. seca
x - tana x
f)
\)- csc 6g
"-'
sec
sin2x
34.tanrx *
1
_
sin a
sec
37.
lr
\
cosl--xlsecx
tart
\2
q.
I
I
tan2 0
36.sec'0
_
/n
\
\?--xlcosx
I
38. cotl
40. cos t(7 +
csc
6
tanz t)
tao O
*
sec
{
ln Exercises 45-56, factor the expression and use the
fundamental identities to simplify.There is more than one
correct form of each answer.
0
16.
,n. sin(_x)
cos(-"r)
x)
28. cos Btan F
30. sec2 x(1 - sin2 x)
41. sin Btan B * cos B
42,
43. cot u sin u I tan u cos u
44. sin 0 sec 0 * cos 0 csc 0
ln Exercises 15-20, match the trigonometric expression
following.
- I
(e) - tan x
-x
sin
cos2 v
with one of the
(b)
t
-
39.2
I - sinv
: 4, sin.x > 0
ll.tan0:2, sing<0
12. csc 0:
-5, cos I < 0
13.sing:-1, cotd:0
x
-
COS.T
35.
5
tanx: -
cot
csc
1
10, sec x
(d)
stn'-T
JJ.-----;---,
csc-x - r
7-R
2'
(a) sec
coszl(n/2)
1
form of each answer.
6.cotS:-3, srn@:-r'ib
10
14. tan 0 is
-
27. cor 0 sec 0
29. sin @(csc {
+.cscg:1, tan0:]
5, tanx: D. sect:
9. sin(-x)
.1
Exercises 27-44, use the fundamental identities to
- the expression. There is more than one correct
simplify
3.sec0:Jt,
\2
sec2x
ln
cosx:
2.tanx: 3
',\
(c) sin2x
tanx
(e) sec2x (f) sec2x *
(b)
tan2x
22. coszx(sec2x 24. cot -r sec -r
1)
45.tan2x-tanzxsin2x
46. sin2 x cscz x - sin2 x
47. sinz x secz x - sin2 x
48. cos2 x * cosz x tan2 x
sec2x - I
_
secx - 1
cos2x - 4
5U.cosx - z^
51.tanaxt2tan2x*l
52. 1 - 2cos2 x * cosax
53. sina x - cos4 x
54. seca x - Lar( x
55. csc3r - csc2x - cscx *
56. sec3x - sec2x - secx *
49.
1
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