Download sin =35 37 , tan =12 37 , csc = 1 cos =37 35 , cot =37 12 , sec

Name: __________________
Class:
1 Use the definitions to evaluate the six trigonometric functions of
. In cases in which a radical occurs in a denominator,
rationalize the denominator.
Date: _____________
2 Suppose that ABC is a right triangle with C = 90 .
If AC = 5 and BC = 4 , find the following quantities.
cos A , sin A , tan A
a. cos A =
b. cos A =
c. cos A =
d. cos A =
e. cos A =
4 41 , sin A =
41
41 , sin A =
41
41 , sin A =
41
5 41 , sin A =
41
41 , sin A =
41
5 41 , tan A
41
41 , tan A =
41
41 , tan A =
41
4 41 , tan A
41
41 , tan A =
41
= 4
5
4
5
5
= 4
5
5
4
3 Determine whether the equation is correct by evaluating each
2
side. Do not use a calculator. Note: Notation such as sin stands for
2
( sin )
.
2
sin 60 = cos 30 + sin 30
a. sin cos =
=
b. sin cos =
=
c. sin cos =
=
d. sin cos =
=
e. sin cos =
=
35
37
37 ,
35
1
37
1 ,
35
35
37
35 ,
12
35
37
35 ,
12
35
37
12 ,
37
, tan cot , tan cot , tan cot , tan cot , tan cot = 12 , csc 37
37
=
, sec 12
= 35 , csc 37
= 37 , sec 12
= 12 , csc 37
12
=
, sec 35
= 12 , csc 37
37
=
, sec 35
= 35 , csc 12
12
=
, sec 35
= 1
= 1
a. no
b. yes
4 Determine whether the equation is correct by evaluating each
2
=
=
=
=
12
35
35
12
37
12
37
35
= 2
= 1
2
37
35
37
=
12
=
side. Do not use a calculator. Note: Notation such as sin stands for
.
2
cos 60 = 2 cos 30 + 1
a. no
b. yes
5 Determine whether the equation is correct by evaluating each
2
side. Do not use a calculator. Note: Notation such as sin stands for
2
( sin )
2
2
2
cos 30 + sin 45 + sin 60 = 1 .
a. yes
b. no
6 Determine whether the equation is correct by evaluating each
side. Do not use a calculator.
sin 60 cos 30
a. yes
PAGE 1
2
( sin )
b. no
cos 60 sin 30 = 1
2
Name: __________________
Class:
7 Carry out the indicated operation.
sin cot a. 1
b. 10 Use the given information to determine the value of remaining five
trigonometric functions. (Assume that the angle is acute.) If a
radical appears in the denominator, rationalize the denominator.
cot sin c. 1
d. tan sin e. 2
+ 4 tan a. (tan b. (tan c. (tan d. (tan e. (tan 3)(tan 5)(tan 7)(tan 4)(tan 6)(tan sec 21
+
+
+
+
+
7)
5)
3)
7)
4)
9 Factor the expression.
2
3 sec a. (3 sec b. (3 sec c. (3 sec d. (3 sec e. (3 sec + 10 sec cot sin 1)(sec 2)(sec 5)(sec 2)(sec 2)(sec sec 8
+
+
+
+
+
3)
3)
5)
7)
4)
=
c. cos sec =
b. cos =
d. cos sec =
e. cos sec PAGE 2
= 2
3
a. cos 8 Factor the expression.
tan Date: _____________
=
= 2 5 , tan 3
3 5 , csc 2
5 , tan =
3
3 5 , csc 5
5 , tan =
3
3 5 , csc 5
5 , tan =
3
3 5 , csc 5
5 , tan =
3
3 , csc =
5
= 2 5 , cot 5
3
=
2
= 2 5 , cot 5
3
=
2
= 2 5 , cot 5
= 5
2
= 2 5 , cot 5
= 3
5
= 2 5 , cot 3
3
2
=
5 ,
2
=
5 ,
2
=
5 ,
2
=
5 ,
2
= 3 5 ,
2
Name: __________________
Class:
11 Use the given information to determine the value of remaining five
trigonometric functions. (Assume that the angle is acute.) If a
radical appears in the denominator, rationalize the denominator.
Date: _____________
14 Rewrite in terms of sine and cosine, and simplify the expression:
4 sin 2
sin cos B = 24
25
7 , tan B
29
29 , csc B = 29
24
7
7
, tan B
b. sin B =
25
25 , csc B = 25
24
7
7
, tan B
c. sin B =
25
25 , csc B = 25
7
24
1
, tan B
d. sin B =
25
25 , csc B = 25
24
e. sin B = 7 , tan B
25
25 , csc B = 25
24
7
= 24 , cot B = 7 , sec B =
7
24
sin sin b.
sin c.
= 24 , cot B = 7 , sec B =
7
24
4
8
a.
a. sin B =
+ 8
d.
+ 2
2
e.
4
sin + 2
4
4
sin 2
+ 2
8
15 Rewrite in terms of sine and cosine, and simplify the expression:
=
7 , cot B = 24 , sec B =
24
7
=
1 , cot B = 24, sec B =
24
=
7 , cot B = 24 , sec B =
24
7
cos + 1 + 1
cos cos + 1 1
cos c. cot + csc d. 2 cos + 1
a. 1
b. 0
16 Refer to the figure. If find AC .
e. sin cos A = 45 and AB = 40 cm ,
12 Rewrite in terms of sine and cosine, and simplify the expression:
2
cos C cos C 2
sin C
sin C
(Hint: Factor the numerator.)
a. cos(C) sin(C)
b. cos(C) + sin(C)
c.
d. 2cos(C)
e. 2sin(C)
1
cos C sin C
13 Rewrite in terms of sine and cosine, and simplify the expression:
cos sec cot a. csc b. sec c. cos d. cot a. AC = 40 cm
d. AC = 20 3 cm
b. AC = 40 5 cm
e. AC =
c. AC = 20 7 cm
e. sin 17 A ladder 14 ft long leans against a building. The ladder forms
and angle of 45 with the ground. How high up the side of the
building does the ladder reach?
a. 7 2 ft
b.
PAGE 3
5 cm
2 ft
c. 14 ft
d.
7 ft
e. 14 2
ft
Name: __________________
Class:
Date: _____________
18 From a point level with and 1000 ft away from the base of a
monument, the angle of elevation to the top of the monument is
29.35 . Determine the height of the monument to the nearest
foot.
________ ft
22 From a point on ground level, you measure the angle of
elevation to the top of a mountain to be 35 . Then you walk
160 m farther away from the mountain and find that the angle
of elevation is now 15 . Find the height of the mountain.
a. 77.5 m
b. 69 m
19 Find the area of the triangle.
c. 112 m
d. 43 m
e. 75 m
23 In the figure, AB = 16 in . Express x as a function of .
area = ________ in.
2
20 Find the area of the triangle. Use a calculator and round your
final answer to two decimal places.
a. 3 tan b. 16 cos c. 3 cos 16 cos 3 cot 16 tan d. 3 sin e. 16 sin 16 cot 3 tan 24 Use the definitions (not a calculator) to evaluate the six trigonometric functio
of the angle.
180
a. 5.91 cm
b. 1.04 cm
2
2
c. 2.95 cm
d. 2.08 cm
2
e. 11.82 cm
2
2
21 An observer in a lighthouse is 66 ft above the surface of the
water. The observer sees a ship and finds the angle of depression
to be 0.5 . Estimate the distance of the ship from the base of
the lighthouse.
a. 7525 ft
b. 7545 ft
PAGE 4
c. 7585 ft
d. 7605 ft
e. 7565 ft
a. sin 180
csc 180
b. sin 180
csc 180
c. sin 180
csc 180
d. sin 180
csc 180
e. sin 180
csc 180
= 0
cos 180 = 1
is undefined sec 180 = 1
is undefined cos 180 = 1
= 0
sec 180 = 1
= 1
cos 180 = 0
= 1 sec 180 is undefined
= 0
cos 180 = 1
is undefined sec 180 = 1
= 0
cos 180 = 1
= 1 sec 180 is undefined
tan 180
cot 180
tan 180
cot 180
tan 180
cot 180
tan 180
cot 180
tan 180
cot 180
= 0
is undefined
= 0
is undefined
is undefined
= 0
is undefined
= 0
= 0
is undefined
Name: __________________
Class:
Date: _____________
25 Use the definitions (not a calculator) to evaluate the six trigonometric functions
26 Use
of the
the definitions of the trigonometric functions to choose the
angle.
correct table.
990
a. sin( 990 ) = 0
cos( b. sin( cos( c. sin( cos( d. sin( cos( e. sin( cos( 990 ) = 1
990 ) = 1
990 ) = 0
990 ) = 0
990 ) = 1
990 ) = 1
990 ) = 0
990 ) = 1
990 ) = 0
a.
tan( cot( tan( cot( tan( cot( tan( cot( tan( cot( 990
990
990
990
990
990
990
990
990
990
) is undefined
) = 0
) is undefined
) = 0
) = 0
) is undefined
) is undefined
) = 0
) = 0
) is undefined
csc( sec( csc( sec( csc( sec( csc( sec( csc( sec( 990
990
990
990
990
990
990
990
990
990
) = 1
) is undefined
) is undefined
) = 1
) is undefined
) = 1
) = 1
) is undefined
) = 1
) is undefined
sin cos tan 0
0
1
0
90
1
0
1
180
0
1
0
270
0
1
540
0
1
0
sin cos tan 0
1
0
0
90
0
1
undefined
180
1
0
0
270
0
1
undefined
540
0
1
0
sin cos tan 0
0
1
undefined
90
1
undefined 0
180
0
1
270
540
0
1
b.
c.
1
undefined
undefined 0
1
0
..to be continued
PAGE 5
Name: __________________
Class:
continuation
Date: _____________
29 Evaluate the expression using the concept of a reference angle.
d.
sin( sin cos tan 0
0
1
0
90
0
undefined
180
0
1
0
270
0
undefined
540
0
1
0
1
1
1
2
a. b.
510 )
1
5
5
d.
5
c. 1
2
cos 675 =
cos( cos tan 0
0
1
0
90
1
0
undefined
180
0
1
0
270
0
undefined
540
0
1
675 ) =
sin 675 =
sin 1
5
2
30 Evaluate each expression using the concept of a reference angle.
e.
e.
sin( 675 ) =
31 Evaluate the expression using the concept of a reference angle.
cot( 600 )
a. 3
5
0
b.
c.
3
3
d. 5
5
e. 1
5
3
3
27 Evaluate the expression using the concept of a reference angle.
32 Evaluate the expression using the concept of a reference angle.
cos 135
tan 510
1
a.
7
b.
7
2
2
2
c. 2
2
d. 2
7
e. a.
b. 2
3
3
3
2
d.
2
c.
1
2
e. 3
3
28 Evaluate the expression using the concept of a reference angle.
cos( 1
6
6
b.
6
a. PAGE 6
33 Use the given information to determine the area of the triangle.
480 )
c.
d. 1
2
e. 1
2
6
2
Two of the sides are 3 m and 6 m, and the included angle is
150 .