Download 7. y= (0.8ff ~-2 : 1016 Student Resources

Graph the function. State the domain and range.
8,1The variables x and yvaxy inversely. Use the given values to wri
relating x and y. Then find y when x
3. y = 3" 3 2
1. X=2, y= 10
2. x=~,y=24
3. x= 3, y
Graph the function, State the domain and range.
~,1 peter~fine whether x and y show direct variatiotl, inverse varia
7. y= (0.8ff ~-2
Simpllfythe expression.
10. (2e2~-~
Graph the function. State the domain and range.
2.5
32
1
2.5
4
20
3.5
8.75
14
5
16
5
12.5
16
6.4
12.5
8
20
24
15. y = 1.5e~ ~ i + 3
Evaluate the logarithm without using a culculator.
17. l°g4 -~tb
18. 1og66
19. log5 125
22. 10I°g9
23. log4 16x
Graph the function. State the domain and range.
Simplify the expression.
21. SI°gSx
83 Graph the fu~ction.
24. ~ln5
13. y = ~:2 4
Graph the function. State the domain anti range.
25. y=logTx
27. y=log~x3 3
26, y=logl/z(x 4)
28. y = log~ (x - 2)
x2 + 4x ~ 3
Y-
a- +
8.4 Shnplify the rational expression, ~f possible.
Expand the expression.
2x
2
30, log lOOx
Y
31. In 20xiy2
32. lOg2
Multiply or divide the expressions. S[mplif~ the resulto
22.
34. log7+21ogx 51ogy
33. log420+41og4x
35. 0.51nlO0 2Inx+8lni,
2x2 - x 6 x2 + x
2x2 + 5x + 3 x2 4
Use the change-of-base formula to evaluate the logarithm.
38. log5 100
39. log727
8.5 Add or subtract the expressions. Sin~plify the restflt.
Solve the equation. Check for extraneous solutions.
,I
40. 24x+2= 8x+2
41. (~)" 3= 33x+’
42. 79x= 18
43. In (3x + 7) = In @-- 1)
44. log5 (3X+ 2) 3
45. log6 (x + 9) + log6x = 2
Write an exponential function y = abX whose graph passes through the given
points.
4~. (1, 8), (2, 32)
47. (1, 3), (3, 12)
48. (2, -9), (5, -243) 49. (1, 4), (2, 4)
b
Write a power function y = ax whose
graph passes through the given points.
50. (2, 2),(5, 16]
:
1015
1016 Student Resources
51. (3, 27),(6, 432)
52. (1, 4),(8, 17)
Simplify the complex fraction.
30.
2x~ 1
5+~
L+3
X
8.6 Salve the equation. Check for exlraneous solutions.
7
53. (5,36),(10, 220)
31.
X
14
34. ~+~= ~
x2
35. 2 x+2
Chapter 7
, R 1 The variables x aud y vary inversely. Use the given values to write an equation
, " ~latingxandy. Thenflndywhenx= -5.
7.1 Graphthefunction. State the domaln and range. 1-g. Seemarginforart.
I-, I [
T F! hE
y=(~/\ ! domain:all 2. y=-2o2Xdomain:al’3" Y=3x 3 2 dmnain:4.
domain: all real
real numbers, range: y > 0 real ,umbers, range: y < 0 all real numbers,
ran g e: y > -2
~.~raph
the function. State the domain and range.
5-8. See margin tar a1.
8.
5. y (3-Ix domaia:all 6. y= -2(~1/x domain: allT" y= (0.8)x s 2
realnmnbers,
range:y<O
domain:
all
real
domain: all real
..~ real numbers,~b! range:y>O
1. X=2,Y=-lO
18. lone6 1
7.4 Simp[i~t the ex3)resMon.
22. lO[°g9 9
2]~. 5Iogax ~
19. ]og~ 125 3
20. log314 2~77 -3
23. legal6x 2x
24. e~n5 5
4. x=25,y= 52
3. x= 3,y= 5
X
~,1 Determine whether x and y show direct variation, inverse variation, or neither.
x
y
2.5
4
32
20
5
7.3 Graphthe function. State the domaln andrange. 13 16. See margin for art.
16. y-e~(X-2}+l
15. y=l.5eX+l+3
13. y=0.5e~x domai.: 14. y 2e-x-2
domain:
all
real
numbers,
domain; all real numb,~
all real numbers, range: y > 0 See margin,
range: y> 1
7.4 ~Evaluatethelogarithmwi~houtusfug acalculator- range: V> 3
2. x=~,y=24
y-_ 02
7.3 Sh~plil~ t he expression.
17. log~ 1~6 -2
1
apter 8
x
domain: all real nsmbers except 0,
range: all real numbers except 3
y
2.5
8.75
3.5
5
16
6.4
x
y
4
12.5
8
12.5 ,
3
20
9
24 ! 92
2Z5
27 [ 105
15
0.8
direct variation
ueither
8,2 Graph the function. State the domain and range, g-12. See margin.
x
domaie: all real nlmdlera exeepl 1,
r~.ge: all real m=~bers ~xce~t -2
ll. y=5~ 2
x
12. y= 4x+19
14.
x~ + 4x +3
8,] Graphthe function. 13-16.
Seey margin.
x
13. y x2 4
xZ+l
15. y=X~+2x 3
x+ 2
7.4 Graph the function. State the domain and range. 25-28. See margin for art,
27. y = logsX + 3
28. y : log3 (x -- 2) + l
25. y=logTx domain: 26. y=logx2(x-4)
~
oma
.:
x
>
4,
range:
x > 0, ~ange: all real .umbers
all real numbers
all real numbers
all real numbers
7.5 ]L~pand the expression,
iog~2 + Iogsx- I
2 + 2 fog x- log y
Condense the expression.
8.~,. Simplify the rational expression, if possible.
~/
17. ~ +x 6 x-2 18.
x3-lOOx
19. x~ 5x 84 x-12 20. x~+7x+10
xZ+9x+18 x t 6
x4+2Ox3+lOOX~x "I0 2xz
98 2(x 7)
x(x 4- 10)
Multiply or divide the expressions. Simplify the result.
21. Gx~y 27 4
22.
2x2
x
6
x2+x
x
23.
3x2+15x
¯ (x~ x 30)
33. log~20+4loggx Iog~20x~ 34. log7+2logx 5logyy×z 35. 0.5lnlOO-21nx+Blny
domain: all real numbers exce£t -3,
range: all real nembers except 4
!~iR/
Ik; ; I
I==1
I
,
Ose the change.of-base forraula to evaluate the logar=thm36. 1og25 abu.12.322 37. log480 abo.t 3.161 38. logsl0~0 about2.Stll 39. 1og727 about1,694
7".6 Solve the equation. Check for extraneous sulutions.
(~)x-3 _ 33x+1 1
40. 24x+z 8~+2 ~
41. -- . --
13-16, 25-28. See Additional Answers beginniag on p. AA1.
l
x+l X--1
27. x~
X+I
x+5
28. x+64
42. 7ax=18 aboutO.165
45. log6(x+9)+log~x=2 3
43. ln(3x+7)=ln(x-1)
44. logs(3x+2)=3 ~1
no solutien
7.7 Write an exponential function y = abx whose graph passes through the given
points.
49. (1,4),(2,4)
47. (1,3),(3,12) 3
46. (1,8) (2 32)
y=~ 2~ory=- .(-2) ~8. (2,-9),(5,--243)
y=--1-3x
V=4’1~
y-2 4~
7.7 Write a power function y = ~ whose graph passes through the given Points.
53. (5, 36), (10, 220)
52. (1, 4), (8, 17)
51. (3, 27), (6, 432)
50. (2, 2), (5, 16)
y= 4-
1016 Student Resources
I,~ Add or subtract the expressions. Simplifythe~esuh. 8x~
1 x~+ 4x-4
X 2 (x+6)(~-2)
~
29. ~ A 35z 5
x+2 x 3X lO (x-S/
r
irl
Simplify the complex fraction.
30.
x
2x~l
5+~
X
3
.
(Sx+S)(2x-I 1)
31.~
~+3 3(1 ! 3x}
x
32.
2
x+2
U~
x+l ix 2)(x-7}
x2 x 6
Solve the equation. Check for extraneous solutions.
ExtraVractice 1017
domain: all real numbers except 0,
range: all real numbers except 0
16.
T ] ] }:~ i i I
Ii
~1 !~ T~ i
Ii
~1->
~1:,
1017
For the given password configuration, determine liow many
possible if (a) digits and letters can be repeated, and (hi digi~
cannot be repeated.
Find the distance beVaeen the two points. Then find the midpoint of the line
segment joining the two points.
2. !2, l/, 13, 7
3. ,. f2, 12! !4,
1. 5, O/. 15.4i
Graph the equation. Identity the focus, directrlx, and axis of symmetry of the
parabola.
7. 14xz=-2Iy
1. 8 digits
2. 8 letter
3. 5 letters fo!lowed by 1 digil
4. 2 digit~
Graph the equation. Identify tile radius of the circlet
Find the mnnber of distinguishable lmrmutaiions ~f the lett,
10. CHOCOLATE
II, STIIA¼
9. VANILLA
Write the standard form of the equation of the circle that passes through tile
given point and whose center is at the orighL
Find the number of combinatious.
15. mC9
Graph the equation. Identi~ the vertices, co-vertices, and foci of the ellipse.
y2
Use the binontial theorem to w~’ite the binomial expansion.
19, (p2 + 4
Write an equation of the ellipse with the given characteristics and center
at (0, 01.
24. Co vermx: [0. 10
23. Vertex: (9, O)
Focus: 3, O)
Graph the equation. Identify the vertices, loci, mid asymptotes of the
hyperbola.
you have an equally likely chance of choosing ally integer fr*
Find the probability of the given event.
21. An odd number is chosen.
22. A nlult
Find the probability that a dart thrown at the given target w
region. Assume the dart is equally likely to hit any point insi
25, x2 Y~
Write an equation of the hyperbola with the given loci and vertices.
30. Foci O. 5.{0.5
29. Foci:(2,0) (2,0)
28, Foci:(O, 8),(0,8}
Vertices: O. 3~/2).10.3V2
Vertices:{0, 6), 0.61
Vertices: 1,O/,tI.O
Graph the equatimL Identify the important characteristics of the graph.
31. iX-3)2 + Y~
9
1
32, LX±2)2+ [y
l)2-4
33. Ly
4)
(x+ 1)2
16
Classify the conic section and write its equation in standard form. Then graph
the equation.
35. 9x~+4y~ 72x+16y+16=O
34. x2*yx±2x+2y 7 0
37, x2 6x 4y+17=0
36. 9x~ 4yz+16y-52 0
9x2 43,2 = 36
40. 3/=x-5
9:~-25y~ 225
0.4 Events A and B ace disjoint. Find P(A or B).
2~. P[A) = 0.4, P(B) = 0,15
27. P(A) = 0,3, P(B) = 0,5
Find the indicated probability~ State whether A aud B are dis,
2~. P(A) 0.25
P(B) 0.55
P{A or B) = ?~
P(A and B) 0.2
30. P(A) = 0.52
P(B) = 0.15
P(A or B) 0.67
P(A and B) ~
31. P(A)
P(B)
P{Aor~
P(A an(
~.~ Find tile probability of drawing tile given cards from a stand
52 cards (a) with replacement and (b) without replacement.
33. Ajack, then a3
34. A club, then another clu
Calculale the probability of tossing a coin 15 times and gettil
number of heads.
38. 7
1018 Student Resources
1018
,hap
2. (2, 1),(3, 7)
(5,4)
3. (-12, 12),(14, 4) 4. (12, -1),(18,-9)
~quation. Identify the focus, directrix, and axis of symmetry of tim
6. x2 = 4y
7. ]4x2 = 2ly
~quation. Identify tlle radius of the circle.
=4
10. x2+y2= 14
11. 3x~+3yz=75
8. 12y2 + 3x = 0
18. x2 + = 1
12. 16xz+16gz=4 ~
I0.1
22. Vertex: (0, -5)
Co vertex: (4, O)
4. 2 digits followed by 2 letters
15. (7, I)
16. (-5, 11)
19. 9xz k 4y2 = 576
23. Vertex: (9, O)
Focus: ( 3, O)
, ....
6. (~P~
7. sP9
8. 12P4
Find the number of distinguishable permutations of the letters in the word.
10. CHOCOLATE
11. STRAWBERRY
12. COFFEE
02 Find the number of combinations.
I
"" ’:"
20. 49X~ + 64y2 = 12544
13. 7C3
14. 4C1
15. 10C9
16. 15C6
0.2 Ilse the binomial theorem to write the binomial expansion.
17. (x - 3)~
18. (2x + 3y)4
19. (p~ + 4)5
20. (xa + y2)~
YOU have an equally likely chance of choosing any integer h’om l through 25.
Find the probability of the given event.
24. Co-vertex: (0, 10)
Focus: (8, O)
~quation. Identify the vertices, loci, and asymptotes of file
21. An odd number is chosen.
22. A lnultiple of 3 is cbosen.
Find the probability that a dart thrown at the given target will hit the shaded
region. Assume the dart is equally likely to hit any point inside the target.
27. 49.~ 81x2=3969
26. x2 y2=4
i=l
3. 5 letters followed by 1 digit
9. VANILLA
luation of file ellipse with the given characteristics and center
(4, O)
:ex: (0, 2)
2. 8 letters
5. 5P2
,quation Identifythevertices co-vertices andfocioftheellipse.
=1
1. 8 digits ....
10J Find the number of permutations.
:andard form of the equation of the circle that passes tl~ough the
and whose center is at the origin.
14. (0, 9)
i0.1For the given password configuration, determine how many passwords are
possible if (a) digits and letters can be repeated, and (b) digits and letters
cannot be repeated.
luation of the hyperbola with the given loci and vertices.
, 8),(0,8)
s:(0, 6),(0,6)
29. Pock(2,0),(2,0)
Vertices:(1,0),(L0)
30. Foci:(O, 5),(0,5)
Vertices:(0, 3~2),(0,3~/2)
:quation. Identify the important characteristics o[ the graph.
F2
32, (x + 2)2 + (y 1)2 = 4
33. (y - 4)2
~9=1
(x + 1)z _ 1
conic section and write its equation in standard form. Then graph
k2x+2y-7=0
y~ + 1By- 52 = 0
35. 9xa+4y2 72x+ 16y+16=0
37. x~ 6x 4y+17=0
Events A and B are disjoint. Find P(A or B).
26. P(A) = 0.4, P(B) = 0.15
36
IIS
39. y=x 2
x2+y~-6x 4y i2=0
40. y2=x 5
9x2 25y2= 225 : :
28. P(A) = 0.7, P(B) = 0.21
Find the indicated probability. State whether A and B are disjoint events.
29. P(A) = 0.25
P(B) = 0.55
P(A or B) = ~?
P(AandB)=0.2
30. P(A) = 0.52
P(B) = 0.15
P(A or B) = 0.67
P(AandB)= ?
31. P{A) = 0.54
P(B) = 0,28
P(A or B) = 0.65
P(AandB)= ?~
32. P(A) 0.5
P(B) = 0.4
P(A or B) = ?
P(A and B) 0.3
I0,~ Find the probability of drawing the given cards from a standard deck of
52 cards (a) with replacement and (b) without replacement.
33. A jack, then a 3
=4
27. P(A) = 0.3, P(B) = 0.5
34. A club, then another club
35. A black ace, then a red card
~.6 alculate the probability of tossing a coin 15 times and getting the given
number of heads.
36. 1
37. 4
;
38. 7
39. 15
’
Extra Practice 101g
1019
apt¢g
OL~ Find the mean, median, mode, range, and staudard deviation of t he data set.
2. 16,18,29,30,34,35,35,38,46
1. 5,5,6,9,11,12 14 16,16,16
3.
4
3, 3,4,1,0,0, 3, 2,10,11
4. L7,2.2,1.8,3.0,0.4,1.2,2.8,2.9
6.
5. 4.5,5.7,4.3,6.9, 2.~/5.7,-1.2,3~8
i
For the sequence, describe the pattern, write the next term, and write a rule for
tile t~th term.
124
2. ~,3,1,~ ....
1.9,16,25,36 ....
3. 12.5,7,1.5,
7.2,3.9,2.6, 9.1,2.5,-7.2,3.9,-Z2
~rite the series using summation notation.
Find the mean, median, mode, range, and standard deviation of the given
data set and of the data set obtained by adding the given constant to each data
value.
8. I0, 12, 14, 16, 16, 18, 19; constant:
7. 33, 36, 36, 39, 49, 56; constant: 2
Find the mean, median, mode, range, and standard deviation of the given data
set and of the data set obtained by mtdtiplying each data value by the given
9.
2,-2,5,4,2, 2,8,3;constant:L5
10. 52,52,76,56,67,89,70;constant:3
A normal distribution has a mean of 2.7 and a standard deviation of 0.3. Find
the probability that a randmnly selected x-value from the distribution is in the
given interval.
11. Between 2.4 and 2.7 :
12, Atleast3.0 :
5.~+2+3+4 ]
4. 16+32+40+64+-..+144
~ind the sum of the series.
~. E{3i+2)
7. 24~~
8
8. E "
’l Write a rule [O1" the nth term of the arithmetic sequence¯ Then graph the first
six terms of the seqnence.
10. as= 15, d=6
11. ai0: 78, d= 10
12. a~=-15~,d=
Write a rule for the nth tern] of the arithmetic sequence. Then find ]is.
13, Atmost2.1
13. 11, 20, 29, 38 ....
14. 8, 15, 22, 29 ....
15. 3 ? 5
I 1.4 Identify the type of sainple described. Then tell if the sample is biased. Explain
your reasoning.
14. The owner of a movie rental store wants to know how often her custmners
rent movies. She asks every tenth customer how many movies the customer
:;
Write a rule for the nth term of the arithmetic sequence thai has the two given
terms.
16, a2 = 9, a7 = 37
18, a3
15. A school wants to constth parents about updating its attendance policy. Each
student is sent hoine with a survey for a parent to complete. The school uses
only surveys that are returned withiu one week.
Write a rule for the nth term of the geometric sequence. Then find aI~.
Find the margin of error for a survey that has the given sample size. Round
your answer to the nearest tenth of a percent.
Find the sum of the geometric series.
17. 600
16. 100
18. 2900
19, 5000
Find the sample size required to achieve the given margin of error. Round your
answer to the nearest whole numher.
rise a graphing calculator to find a model for the data. Then graph the model
and the data in the same coordinate plane
24.
25.
0
2
2@1 1
4
6
8
10
12
14
10
3
4
10
14
20
21
36
1
2
3
4
5
6
7
8
0.8
0.8
1.1
3
9
30
90
280
28.
~ Fiad the sum of the infinite geometric series, if it exists.
27.2 4+8- [6 F...
28. 6,75 + 4.5 3
Write the repeating decimal as a fraction in lowest terms.
29. 0.333...
30. 0.998989...
31. 0.21212L..
32. 1.50150
Write a recursive rule for the sequence. The sequence may be arithmetic,
geometric, or neither.
33. 2.5, 5,10,20 ....
34. 2, 2, 6,-10 ....
35. 1,2,2,4,8,32,..
Find "the first three iterates of the function for the given initial value.
36. fix}=2x-5>xo=3
1020 Student Resources
1:~. 64 256
22. ~3/4)i ~ 23. ~0.5(3)i ~ 24. ~10(53)~
26, 8+4+2+1+...
22. ±5.5%
1020
17. as = 10.5, at6 = 18.5
37. f{x) = ~x 2, xo= -10
38. /"x = 3xZ+ v, r~
Chapter 11
11.1 ffindthemean, median, mode, range, andstanda~ddeviatibnofthedataset.
11, 11.5, 16, 1~, 4.313
about 31.Z, 34, 30, 30, 8.90
1, 2, -3, 15, 4.991
2, 2, no mode, 2.5, 0.253
3,45, 4,4, 53, 9, 3.09
-L225, -2.35, -7.2, 13, 5.51~2
11.2 l~ind the mean, median, mode, range, and standard deviation of the given
data set and of the data set obtained by adding the given constant to each data
value.
8. 10, 12, 14, 16, 16, 18, 19; constant; -1
7. 33, 36, 36, 39, ~t9, 56; constant: 2
41.5, 37,5, 36, 23, 8.221; 43.0, 39,5, 38, 23, 8.221
15, 16, Ifi, 9, 2.976; 14, 15, 15, 9, 2.976
11.2 I~ind the mean, median, mode, range, and standard deviation of the given data
set and of the data set obtained by mditlplying each data value by the givnn
constant.
~I --2, --215, 4, 2, --2, 8, 3; constant: 1.5
10. 52, 52, 76, 56, 67, 89, 70; constant: 3
2, 2.5, -2, 10, 3.5; 3, 3,75, -3, 15, 5.25
66, 67, 52, 37, 1235 190 201,156,’ 1,38 25
!1.3 A normal distribution has a mean of 2.7 and a standard deviation of 0.3. ]~ind
the probaldlity that a randomly selected x-value from the distribution is in the
givenlnterval. .
11. Between 2.4 and 2.7 0.34
12. Atleast3.0 2.16
32 : 9; 49; an = (n + 2)z
1. perfect squares beginniug with
For tile sequence, describe the pattern, write the next term, and write a rule for
the nth term. 1-3. See mmgiu.
1 2 41,~ ....
2. 5,g,
I. 9,16,25,36 ....
3. 12.5, 7, 1.5, -4 ....
2. tmdiiples of ; ; a, - 3
3. each term is decreased by 5.5;
-9.5; a, = !8 - 5.5n
~f t~rite the series using summation notation.
~, Find the sum of the series.
~ WrRe a rule for the nth term of the arithmetic sequence. Then graph the first
sixterms of the sequence. ~0-12. See lU~lOia 10[ ~rt.
~rite ar~e ~r the nth term of the arithmetic sequence~ Then find a]~i
13. Atmost2.l 0.025
11.4 Identif~thet3,peofsampledescribed.Thentellifthesampleisbiased.Explain
your reasoning.
14. The owner of a movie rental store wants to know how often her customers
rent movies. She asks every tenth customer how many movies tile customer
rents each month. Systematic; aot biased; the owner took a raodolll selectioa of costomers.
15. A school wants to consult parents about updating its attendance policy. Each
student is sent home wittl a survey for a parent to complete. The school uses
only surveys that are returned within one week. Sail-selected; biased; 0nly tb0sa parents
~dte a r~e for ~e nth te~ of the ~tthmetic sequence that has the two given
terms.
Write a rate for the nth term of the geometric sequence. Then find ale.
itt
% = ~ ~, ’ i~.r~3
F~d~es~ofthegeome~icseries.
18. 2900 ± L9%
19. 5000
11.4 Find the sample Size required to achieve the given margin of error. Round your
answer to the nearest whale number.
21. ±2% 2500
20. ±1% 10,000
22. ±5.5% 331
23. ±6.2% 260
11.5 Use a graphing calculator to find a model for the data. Then graph the model
and the data in the same coordinate plone. 24-2fi. See margio for alt.
~ ~ind the sum of the Infinite geometric series, if it exists.
~6. 8+4+2+1+... 16
27. 2~4+8 16+...
Write the repeating decimal as a fraction in lewest terms.
30. 0,898989... 8~
7
Write a recursive rule for the sequence. The sequence may be arithmetic,
geometric, or neither.
33. 2.5, 5, 10, 20,...
34. 2, -2, -6, -i0,,..
35. I, 2, 2, 4, 8, 32 ....
md the first three iterates of the function for the given initial value.
y
0.5
0.8
1.1 I 3 I 9 [ 30 :1 90
280 I
S6. f(x)=2x
1020 Student Resources
5, xo ~ 3
L ~-3,-H
37. f(x) = 54x-2, xo= 10
-I0, 10, 10
"
~’" -
-
38. f(x) ~ 3x~ + x, xo= l
2, 14, ~02
Extra Praotice 1021
1021
Let 0 be an acute angle of a right triangle. Find the values of the oilier five
trigonometric functions of O.
ill Graph the fmiction.
2. ,= 3sinx
!. sin0=~
5
2. tan0= 15
8
8. sec0=2
Graph the Mne or cosine function.
liL%l SolveAABCusingthediagramandthegivenmeasuremenis.
5. A=21°,c=8
7. B=60°,c=20
7. y=2*
6. B= 66°,a = 14
8. A=29~,b=6
10. B=56°,c=7
9. A= 18°,c= 18
1,~ Graph the tangent function.
A
8. y=2tanx+ 2
l ’~.:!~ Convert the degree measure to radians or the radian measure to degrees.
Simplify the expression.
4
6
~7~,2 Find the arc length and area of a sector with the given radius r and central
angle O.
15. r=Sft, 9 90° ......
16. r=2in.,9 300°
12, (seca l)(scc x + i)
tanx
13. tan[~
Verify tile identity.
113.3 Sketch the angle. Then find its reference hngle.
19. 30°
18. 250°
Find the general solution of the equation.
20. 8vr
3
6
L~,,~ Evahlate the function without using a calculator.
22, sin (--60°)
23. CSC 240°
24. tall ~4~
17. 12tanZx 4 0
18. 3sinx
2sinx ~3
19. tanZx
Solve the equation in the given interval. Cheek your solutions.
25. COS(5~)
~ILA Evaluate the expression without using a calculator. Give your answer in both
radians and degrees.
L5 Write a ftmction for tile sinusoid.
24,
25.
1 ..,, Solve the equation for 0.
30. sin0- 6.2~,90 <0<180° 31. cos0~0.9;270°<0<360° 32. tan0=2;180°<O<270:
ILL!> Solve&ABC. (Hint:Someofthe"triangles"lnayhavenosolutionandsome
may have two solutiolls.)
35. B=86°,b= 13, c=11
33. A=B4°,a=B,b=7
34. A=50<’,C=B5°,b=60
II ::.[~ FindtheareaofAABCwiththeglvensidelengthsandincludedangle,
36. A = 35°, b = 50, c ~ 120
38. C = 20°, a = 10, b = 16
37. B = 35°, a = 7, c = 12
Find the exact value of the expression.
26. sill ( 15°)
27. cos I65~
28. tan ll~r
29
Find the exact vahms of sin 2a, cos 2a, and tan 2a.
VL~ Solve &ABC.
3K a =16, b = 23, c =17
40. C = 50°, a =12, b =14
41. A = 80°, b = 7, c=5
Find the general solution o f the equation,
i)!;.6 Find the area of AABC with the given side lengths,
42. a=6, b=3, c=4
1022 Student Resources
1022
43. a=14, b=30, c=27
44. a=16, b=16, c=20
33. cos2x cosx= 0
34. cos x = sinx
2
35. sin 2x
Chapter 13
[:Mpter 14
( 13.1 ’Let O be an acute angle of a right triangle. Find the values of the other five
trigonometric functions of 0, 1 4, See margin.
1. sinO=~
5
=~
2. tanO15
3. secO=2
,~Graph the function. 1-~. See margin.
4. cosO=~
4
13.1 Solve A ABC using the diagram and the given measurements.
5. A= °,
21°,c= 8
6. B~ 66°,a=
14
B = 69 a ~ 2.867, b ~ 7.469
,4 = 24°, b ~ 31.LI45, c ~ 34.q20
A = 30°, a = 16, b = 10\ 3
61 , a ~ 3.326, c ~, 6,860
10. B = 56°, c = 7
9. A = 18°, c = 18
A
h
B=72°,a~5.562, b~-17.119
A=34°,a~3.B14, b~5.803
13.2 Convert the degree measure to radians or the radian measure to degrees.
(" 1. y=cos¼x
2. y=3sinx
/ 5, Y= sin 2(x- ~)+I
3. y = sin 2~rx
6. y = -sin(x + ~)
4. y = 2 tan2x
7. y=2cosx+3
j,] Slmplifythe expression.
11.
13.2 Find the arc length and area of a sector with the given radius r and central
angle O.
15. r 5ft, 0=90 it, ft 16. r=21n.,0=300°
12~cm, 72~- cmz
(2 )
(-x) I 12.
tanx
Verlf~the identity. 14-16. See margin.
cos { ~
16. 2 secZx ~ l - tanax
13.3’ Sketch the angle~ Then find its referenee~angle.
Find the general solution of the equation.
17. 12tan2x=4=O
5w
lB. 3sinx= 2sinx+3
19. tanZx 2tanx=-I
,,.13.3 Evaluate the innction without using a calculatur.
25. cos(
21, 2 2cosZx=3+Ssinx;O~x<2~r 7a
5’ 5
23. cos2x 4cosx+l=O;O_<x<w abotfll.2995
13.4 Evaluate the expression without using a calculator. Give your answer in both
radians and degrees.
26. sin ~0 O,O~
13.4 Solve the equation for 0.
~,~ Write a function for the sinusoid.
27, COS-I -56~,
28. cos-13 tlildelill~,d
29. tan ~1 ~,~
30. sinO= 0.25;90°<0<180~
31. cosO= 0.9;270°<0<360°
32. tanO=2;180°<O<270°
about 165.52"
about 334.16°
illlou124343
13.5 Solve AABC. (Hint: Some of the "triangles" may have no solution and some
may have two sulutlons.)
33. A = 34°, a : 6, b = 7
34. A = 50°, C = B5°, b = 60
35. B = B6°, b =13, c = ll
See margin.
B = 65~, a ~ Gfl.71, c = 60
A ~: 36.4°, C ~ 57.G~, a : 773
13.~ Find the area of AABCwlth the given side lengths and included angle.
36. A=35°,b=50, c=120
37. B=35°ia=7, c=12
38. C=20°,a=lO, b=16
about 27.4
about 1728
about 24.1
13.6 Solve AABc.
~ 40.7°, C~ 105.3°, c = 10.35
139.3°, C~ 6.7°, c ~ 1.25°
39. a= 16, b=23, c=17
40. C=50°,a= 12, b=14
A~4&i°,B- 88,3°,C-47,~° A--55.7°,B~ 74.3°,c:= ~l.14
13.6 Find the area of AABC with the given side lengths.
42. a=6, b=3, c=4
about 5.33
1022 Student Resources
43. a=14, b=30, c=27
about 189
41. A=80°,b=7, c=5
~,$ Find the exact value of the expression.
26. 8in[-15°) \2~ \6 27. Cos165° ~-\6~ 28. tanllt2~r . 2+ ,~
~,7 Find the exact values of sin 2a, cos 2a, and tan 2~.
3~r
cosa= l~o,O<a<~
13’ 13’ 5
riudthegeneralsointionoftheequatinn.
44. a = 16, b = 16 c = 20
about 25
33. G~S2X cOSX=0
34.
32. sina= 3.,3_*r<a<2~r _2zl 7 24
1!1 31 "19
50 ’ 50’-31
cos~= sinx
5~
Extra Practice 1023
,. /
1023