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Chapter 5
Analytic Trigonometry
VOCABULARY CHECK: Fill in the blank to complete the trigonometric identity.
1. sin(z - v) :
2. cos(z * u) -
3. tan(u * u) 5. cos(z - y) _
* u) 6. tan(u - v) :
4. sin(z
!n Exercises 1-6,find the exact value of each expression.
1. (a)
cos( 120"
+
45")
2. (a) sin(135o - 30)
3. (a)
."'(; .;)
(b) cos 120" +
-(b)
cos 45o
sin 135o - cos
30o
ft)
\/ .or34 + cos3
.
- cos 3 sin 1.2
! ---28. .o, 3.o, 4 - sin
7 5 ---- 7 ,in!
5
27
29.
3
4. (a)
r,r(?.?)
s. (a)
",(? -;)
(u)
\/
,irE4 + sin&
6
,inU - 7r
6-sm;
(b) sin 315' - sin 60o
66)
\/
6. (a) sin(3 l5o - 60')
ln Exercises 7-22,find the exact values of the sine, cosine,
and tangent of the angle by using a sum or difference
formula.
+ 45o
225o - 30o
7r
11.
-Y +
t246
ITrr
rt
^v'n46 _9n _5rr
1.4.
15. 295'
1.6.
17.
Lg. 150
7. 105":
9, 195' :
Llrr
lg.
-
60o
165"
l3rr
8.
L0.
12.
20.
12
2r. -L3rr
t2
22.
165o:135'+30o
255":300o-45o
7rr rr
1234
I
I
iT
1264
-
105"
_7n
t2
5rr
L2
ln Exercises 23-30, write the expression as the sine, cosine,
or tangent of an angle.
23. cos 25o cos l5o
24. sin
^
-
tan 325o
1
26.
140o cos
+
-
sin 25o sin 15o
50' + cos 140o sin 50o
-
tan 86o
tan 325o tan 86o
tan L40o - tan 60o
1
*
tan I40" tan 60o
sin 3 cos 1 .2
tan 2x
1
-
tan
*
tan x
Zxtanx
30. cos 3x cos 2y
*
sin 3x sin Zy
ln Exercises 31-36, find the exact value of the expression.
3L. sin 330o cos 30o - cos 330o sin 30o
32, cos 15o cos 60o + sin 15" sin 60"
33.
sinf;""tf *
cos
34..orfr.orff 35.
36.
tan 25"
1
+
sin
#rr"I
*
tan I 10'
tan 25" tan 110o
tan(5
1
#t"i
n/4)
tan(5
-
tan(rr/12)
rr/4) tan(rrltZ)
ln Exercises 37-44,find the exact value of the trigonometric
function given that sin u = * and cos y = -3. Goth u and
y are in Quadrant ll.)
37. sin(z + ,)
39. cos(z
- y)
40. sin(u - u)
42. csc(z - y)
38. cos(z
+ ,)
41. tan(u + ,)
43. sec(v
-
44. cot(u + v)
u)
ln Exercises 45-50,find the exact value of the trigonometric
function given that sin u
and y are in Quadrant lll.)
= -*
and cos y
=
45. cos(z
+
v)
46. sin(z
47. tan(u
-
y)
49. sec(z
+ ,)
- u)
50. cos(z - y)
48. cot(u
+
v)
-
1. (Both u