Download Ch 6/7/8 Exam Review Convert the angle to a decimal in degrees

Ch 6/7/8 Exam Review
12) tan
Convert the angle to a decimal in degrees. Round the
answer to two decimal places.
1) 90°52'19''
< 0,
sin
<0
In the problem, sin and cos are given. Find the exact
value of the indicated trigonometric function.
5
2
, cos =
Find sec .
13) sin =
3
3
Convert the angle to D° M' S'' form. Round the answer to
the nearest second.
2) 13.79°
Use the properties of the trigonometric functions to find
the exact value of the expression. Do not use a calculator.
14) sec2 70° - tan2 70°
If s denotes the length of the arc of a circle of radius r
subtended by a central angle , find the missing quantity.
3) r = 9.6 inches, = 315°, s = ?
Convert the angle in degrees to radians. Express the
answer as multiple of .
4) -60°
Find the exact value of the indicated trigonometric
function of .
3
in quadrant III
Find cot .
15) csc = - ,
2
Convert the angle in radians to degrees.
8
5)
5
Graph the sinusoidal function.
16) y = 4 sin (3x)
If A denotes the area of the sector of a circle of radius r
formed by the central angle , find the missing quantity. If
necessary, round the answer to two decimal places.
6)
=
4
radians, A = 99 square meters, r = ?
In the problem, t is a real number and P = (x, y) is the
point on the unit circle that corresponds to t. Find the exact
value of the indicated trigonometric function of t.
5
39
)
Find tan t.
7) ( ,
8 8
Graph the function.
A point on the terminal side of an angle is given. Find
the exact value of the indicated trigonometric function of
.
8) (-2, -3)
Find tan .
17) y = -3 tan
Solve the problem.
9) What is the domain of the sine function?
Use the fact that the trigonometric functions are periodic
to find the exact value of the expression. Do not use a
calculator.
10) tan 390°
Name the quadrant in which the angle
11) cos < 0, csc < 0
lies.
1
1
x
4
Find the phase shift of the function.
18) y = 4 cos -2x -
28) csc-1 2
3
Solve the equation on the interval 0
29) 2 cos + 3 = 2
Graph the function.
19) y = csc x +
30) 4 sin2
5
<2 .
-3=0
31) 2 cos(2 ) =
3
Solve the equation on the interval [0, 2 ).
32) Suppose f(x) = cos - 1. Solve f(x) = 0.
Solve the equation on the interval 0
2
=
33) cos 2 2
2
34) cos2
35) 2 sin2
Find the exact value of the expression.
2
20) sin-1
2
36) tan
38) 3 cot2
Find the exact value of the expression. Do not use a
calculator.
3
22) cos-1 cos 5
23) tan-1 tan -
+1=0
- 3 sin
+ sec
37) sin2
21) tan-1 (-1)
-2=0
=1
- cos2
+ cos
- 4 csc
=0
=1
Establish the identity.
39) sin2 (- ) + cos2 (- ) = 1
40) (sin x)(tan x cos x - cot x cos x) = 1 - 2 cos 2 x
8
41) (tan v + 1)2 + (tan v - 1)2 = 2 sec2 v
Find the inverse function f-1 of the function f.
24) f(x) = 8 cos x + 2
42)
Find the exact value of the expression.
3
25) sec sin-1 2
26) tan cos-1 -
+ 2 cos
<2 .
tan u - 1 1 - cot u
=
tan u + 1 1 + cot u
43) 1 -
1
2
44)
27) sec-1 2
2
cos2 u
= - sin u
1 - sin u
csc + cot
tan + sin
= csc
cot
45)
sin
csc
+ sin
+ csc
= sin
Use the information given about the angle , 0
2 , to
find the exact value of the indicated trigonometric
function.
24
, 0< <
Find cos(2 ).
58) sin =
25
2
sin
46) cos x csc x tan x = 1
47)
cot 2 x
1 - sin x
=
csc x + 1
sin x
59) sec
48) sin3 x cos2 x = sin x (cos2 x - cos4 x)
in quadrant II. The point -
12
52)
9
sin
18
- cos
18
sin
9
61) sec(2 )=
Find cos ( - ).
=
1
,
4
value of sin
63) cos
in quadrant II, find the exact
-
6
=
in
csc2
csc2 - 2
5
cos
2
2
Express the sum or difference as a product of sines and/or
cosines.
64) cos(7 ) - cos(3 )
3
65) sin(6 ) - sin(4 )
Establish the identity.
55) cos x +
1
, y , on the circle
3
Express the product as a sum containing only sines or
cosines.
62) sin(9 ) cos(5 )
Find the exact value under the given conditions.
4
2
< < ; cos = , 0 < <
53) sin = ,
5 2
5
2
54) If sin
Find sin(2 ).
Establish the identity.
tan 160° - tan 40°
1 + tan 160° tan 40°
Solve the problem.
>0
x 2 + y2 = 1, also lies on the terminal side of an angle
quadrant III.
60) f(2 )
50) sin 165°
51) cos
6 11
, csc
11
Given that f(x) = sin x, g(x) = cos x, and h(x) = tan x,
evaluate the given function. The point (x, 3), on the
circle x 2 + y2 = 7, also lies on the terminal side of an angle
Find the exact value of the expression.
49) cos
=-
3
1
cos x - sin x
2
2
Find the value of the indicated trigonometric function of
the angle in the figure. Give an exact answer with a
rational denominator.
66)
Find the exact value of the expression.
4
3
56) cos tan-1 - sin-1
3
5
Solve the equation on the interval 0
57) sin = - 2 - cos
9
<2 .
Find sin .
3
5
67)
10
7
Find cot .
Find the exact value of the expression. Do not use a
calculator.
68) csc2 60° - tan2 30°
Solve the right triangle using the information given.
Round answers to two decimal places, if necessary.
69) a = 8, B = 25°; Find b, c, and A.
70) a = 3, c = 6; Find b, A, and B.
Solve the problem.
71) A surveyor is measuring the distance across a
small lake. He has set up his transit on one side
of the lake 90 feet from a piling that is directly
across from a pier on the other side of the lake.
From his transit, the angle between the piling
and the pier is 40°. What is the distance
between the piling and the pier to the nearest
foot?
4
Answer Key
Testname: CH 6 AND 7 AND 8 EXAM REVIEW
1) 90.87°
2) 13°47'24''
3) 52.8 in.
4) -
3
5) 288°
6) 15.88 m
39
7)
5
8)
3
2
9) all real numbers
3
10)
3
11) III
12) IV
3
13)
2
14) 1
15)
5
2
16)
5
Answer Key
Testname: CH 6 AND 7 AND 8 EXAM REVIEW
17)
18)
6
units to the left
19)
20)
4
21) 22)
4
3
5
23) -
8
x-2
24) f-1 (x) = cos-1
8
25) 2
26) - 3
27)
28)
3
6
6
Answer Key
Testname: CH 6 AND 7 AND 8 EXAM REVIEW
29)
30)
31)
2 4
,
3 3
3
2 4
5
,
,
3 3
3
,
11 13 23
,
,
12 12 12
,
12
32) {0}
3 9
11
,
,
33)
8 8
8
34) { }
35)
,
6
36) {0}
1
6
37) 0,
2
4
,
3
3
38)
,
6
5
6
39) sin2 (- ) + cos2 (- ) = (-sin )2 + (cos )2 = sin2
+ cos2 = 1
sin x cos x cos 2 x
= sin 2 x - cos 2 x = (1 - cos 2 x)- cos 2 x = 1 - 2 cos 2 x.
40) (sin x)(tan x cos x + cot x cos x) = sin x
cos x
sin x
41) (tan v + 1)2 + (tan v - 1)2 = tan2 v + 2 tan v + 1 + tan2 v - 2 tan v + 1 = 2(tan2 v + 1) = 2 sec2 v
1
1 - cot u
-1
cot
u
cot u
tan u - 1
1 - cot u
=
=
=
42)
tan u + 1
1
1 + cot u
1 + cot u
+1
cot u
cot u
43) 1 -
cos2 u
1 - sin2 u
(1 - sin u)(1 + sin u)
=1=1= 1 - (1 + sin u) = - sin u
1 - sin u
1 - sin u
1 - sin u
44)
csc + cot
tan + sin
45)
sin
csc
+ sin
+ csc
=
=
1
sin
sin
cos
sin
1
sin
+
=
+ sin
+ sin
1
+
sin
46) cos x csc x tan x = (cos x)
47)
cos
sin
1
sinx
=
1 + cos
sin
sin
+ sin
cos
sin + sin
sin + sin
sin sin
cos
= (sin
=
1 + cos
sin
+ sin ) ·
cos
1
=
sin (1 + cos ) sin
sin sin
sin + sin
= sin
sin x
= 1.
cos x
cot 2 x
csc2 x - 1 (csc x + 1)(csc x - 1)
1
sin x 1 - sin x
.
=
=
= csc x - 1 =
=
csc x + 1
csc x + 1
csc x + 1
sin x sin x
sin x
48) sin3 x cos2 x = sin x (1 - cos2 x) (cos2 x) = sin x (cos2 x - cos4 x).
2( 3 - 1)
49)
4
50)
·
2( 3 - 1)
4
7
sin
·
cos
sin
= csc
cot
Answer Key
Testname: CH 6 AND 7 AND 8 EXAM REVIEW
51)
1
2
52) - 3
-6 + 4 21
53)
25
54)
1+3 5
8
55) cos x +
56)
= cos x cos
6
- sin x sin
6
=
3
1
cos x - sin x.
2
2
24
25
57)
4
58) 59)
6
527
625
-5 11
18
60) -
4 3
7
61) sec(2 ) =
1
1
=
cos(2 ) 1 - 2 sin2
62)
1
[sin(14 ) + sin(4 )]
2
63)
1
[cos(2 ) + cos(3 )]
2
=
1
sin2
1
sin2
-2
=
csc2
csc2 - 2
64) -2 sin(5 ) sin(2 )
65) 2 sin cos(5 )
9 106
66) sin =
106
67) cot
=
7
10
68) 1
69) b = 3.73
c = 8.83
A = 65°
70) b = 5.2
A = 30°
B = 60°
71) 76 ft
8