Name: __________________
Class:
1 Use the addition formulas for sine and cosine to simplify the
expression.
sin 47 cos 17 cos 47 sin 17
2 Simplify the expression.
cos
3
2
+
a. sin
3
2
3
2
b. sin
c. sin +
d. +
e. cos sin a. b. )
cos 1
c. sin d. sin e. cos 4 Use the formula for cos(s + t ) to compute the exact value
of cos 75 .
a.
b.
c.
6 + 2
4
3 + 2
4
6 2
4
3
d.
4
3 e.
5 Use the formula for sin(s of sin
a.
b.
c.
.
12
3
4
3 d.
2
2
4
a. sin 105 =
cos 105 =
2
4
b. sin 105 =
cos 105 =
2
2
2
cos 105 =
2
4
e.
6 +
4
6 4
2
2
3 + 1)
1)
= 12
13
cos = 8
17
) =
) =
1)
3 3 + 1)
(
3 + 1)
1)
3 (
3 + 1)
(
3 1)
) and cos(
where sin (
(
(
2
4
cos 105 = cos(
(
2
4
e. sin 105 =
1)
3 3 2
4
4
t ) to compute the exact value
(
2
4
and cos 105 .
3 + 1)
2
4
d. sin 105 =
7 Compute sin(
below.
(
(
2
2
c. sin 105 =
sin(
4
3 + 2
4
PAGE 1
6 Determine the exact value of sin 105
cos 105 = 3 Simplify the expression.
cos(
Date: _____________
2
where <
< ) using the data
<
< 3
2
Name: __________________
8 Suppose that cos Compute sin ) .)
a. sin cos 2
= = b. sin = cos 2
= c. sin = cos 2
=
Class:
Date: _____________
5 and 3
< < 2 .
13
2
and cos 2 . (Hint: cos 2 = cos( +
11 Use the given information to compute cos
=
3
5
7
25
12
13
119
169
3
5
d. sin cos 2
e. sin cos 2
= 12
13
b.
7
25
a.
b. tan s = 3 and tan t = 5
a. tan (s + t ) =
1
8
t) = b. tan (s + t ) =
2
5
8
c. tan (s + t ) = 1
7
tan (s t ) = 4
tan (s t) = d. tan (s + t ) =
5
13
b. PAGE 2
13
4
17
5
d.
5
8
1
5
and
90 < 4 6
25
4 5
d.
25
11
12
e. c.
4 6
25
366
391
119
b.
120
e. 12
13
213
391
120
d.
169
c.
e.
.
< 180
1
8
a.
< s < 3
2
c.
= 187
14
182
14
d. 4
7
7
e. tan (s + t ) = 4
8
tan (s t ) = 1
sin 2s = ?
a.
e.
t) = 10 Use the following information to evaluate the expression.
cot s = 5
10
17
c.
2
< 2
13 Refer to the triangle and compute cos 2t .
tan (s 2
5
<
12 Use the given information to compute sin 2
cos 4
7
3
2
and
14
17
143
17
a. = 119
169
= 12
13
119
=
169
9 Use the given information to compute tan(s + t ) and
tan(s t ) .
tan (s = 6
7
cos 119
169
8
25
.
Name: __________________
Class:
14 Refer to the triangle and compute tan
a.
3
4
4 + 5
5
b.
3
5
c.
s
2
Date: _____________
.
e.
3 5
5
4
5
d.
15 Simplify the following expression.
sin 2
sin cos 2
cos a. cos b. csc c. sin d. cot e. sec 4
16 Express sin in a form that does not involve powers of the
trigonometric functions.
a.
b.
c.
d.
e.
1 + 3 cos 2
9
1 4 cos 2
8
3 4 cos 2
8
3 + cos 2 8
1 + 4 cos 2
9
+ cos 4
cos 4
+ cos 4
cos 4
+ cos 4
17 Simplify the following expression.
2csc 2
2
a.
csc cot b.
sec cot 2
c.
sec cot sin d.
csc tan 2
PAGE 3
2
e. sec tan