_____
NAME
O
DATE
SCORE
Cumulative Test Chapters 7—9
ANSWERS
Directions: Write answers in the spaces provided.
1.
(4)
1. Express —165° in radians; leave in terms of it.
2.
(4)
2. Find the area of a circular sector with arc length 6 and central angle 2
radians.
3.
(4)
Complete the following with the best answer.
3. If 9 is a third-quadrant angle, and sin 9=
4. Sketch the graph of y
=
Icos xl for 0
x
—
<
.4 find cos
9.
4.
—
—
—
—
—
—
—
— —
—
-ø
0
2nX
it
5. Express cot 135° in terms of a reference angle.
(
6. If tan x =
where 0
—
(4)
2it.
y
—1
(See graph)
x < 2it find sin x.
5.
(4)
6.
(4)
7.
(4)
8.
(4)
9.
(4)
10.
(4)
11.
(4)
7. Find the exact value of csc (Sin-’
8. Give the domain and range of y = Tan-’ x.
9. Solve csc 9= —5 for 0°
9< 360° to the nearest tenth of a degree.
10. Find the inclination of the line 4x
11. Give the equation of the
following graph in terms
ofsine.
—
=4 to the nearest degree;
12. Sketch the graph of
(
i
y=1—3cosx÷
.
12.
(See graph)
(4)
13.
(4)
14.
(4)
y
—2
0
13. Simplify
1
+
1
tan 9 I
2
14. Simplify cos(
—
+
—
—
—
—
—
—
It
2it
X
cot 9.
0] cot 0.
(continued)
TESTSfor ADVANCED MATHEMATICS
—25—
Copyright © by Houghton Mifflin Company.
All rights reserved.
_
NAME
DATE
SCORE
Test Chapters 7—9 (continued)
ANSWERS
Solve for 0
15 (See question)
(4)
16.
(4)
17.
(4)
18
(4
x <2it. Leave your answer in terms of it.
15. 4cosx=3secx
16. 2 sin
x + sin x
2
—
1 =0
17. Find the measure, to the nearest tenth of a degree, of the vertex angle
of an isosceles triangle with a base of length 8 and legs of length 5.
18. An airplane is at an elevation of 30,000 ft and approaches the airport
with an angle of descent of 50• What is the distance between the
airport and the point on the ground directly below the airplane?
(Round to three signflcant digits.)
19.
19. The area of /ABC is 45 square units: If a = 10 and b = 15, find the
measure of angle C to the nearest degree.
.
(4)
21.
(4)
Given the diagram below:
(4)
-
V
•
::____
_
20. Find the measure of Z Y. (Round to the nearest tenth ofa degree.)
21. Find ZN. Round to the nearest whole unit.)
24.
(4)
22. Find the area of L.XYZ. (Round to the nearest square unit.)
25.
(4)
23. Find the perimeter, to the nearest tenth, of a regular octagon inscribed
in a circle of radius 6 inches.
24. An airplane flies on a course of 100° at a speed of 1100 km/h. How
far east of its starting point will it be after 2 hours? (Round to the
nearest kilometer.)
25. Ashipproceedsonacourseof280°for3hoursataspeedofl2
knots, then changes to a course to 200° for 2 more hours. How far is
the ship from its starting point? (Round to the nearest nautical mile.)
TESISforADVANCED MATHEMATiCS
—26
—
Copyright © by Houghton Mifflin Company.
All rights reservecL
DATE._________
NAME.
.
TestChapter:1O.
SCORE
ANSWERS..
(3)
DIrectIons. Write answers in the spaces provided.
Classify. each of the follOwing as alWays. sometimes, or never trues
2.
(3).
2:.
(3).
3. Iftana=3andtanj3=2,thentan(a+fl)=5
4.
(3).
4. When you use the half-angle formulas, you choose whether to use +
or— by noting in which quadrant the angle lies
5.
(3),
5. Using a graphing utility (or graphing calculator) to solve a system of
tngonometnc equations yields exact results
6
(3)::
7.
(3)
1. sin2x=2sinx
2 cos(+.o)=—sinO
Solver
6. Use a sum formula to find sin 75° in simplest radical form..
8
S1mpIIfy
7 s1nxcos(x+y)cosxsin(x+y)
9,.
.
(4)
8. coa(!!+x)+cos(!!_x)
(
t
9 Evaluate tan
(!
-
1(L Use a sum or difference formula to find tan 345.° m simplest radical form..
11, Fmd the two supplementary angles betweeny = 2x +3 andy =1— 3x
If 0
a<
and sin a =
13 cos2a
12. sin2a
11.
(4)
12:
(4)c
13.
(4)
14 cos4cc
14.
(4)
15.
(4)
16..
(4)
17.
(4)
18.
(4)
19.
(4)
evaluate the following without using tables or a calculator..
16.
15. tan2ft
tan 313
SImpllfy
2
17. cos
(4)
evaluate the following without using tables
or a calculator
If tan 13 =
10’
x) if tan x =
()
—
18. 2 cos
2 (3A)
2
sin
—
()
1
sin2x
1+cos2x
(continued)
TFSTSJorADVANCED MATHEMATICS
—27—
Copyright © by Houghton Muffin Company.
All rights reserved.
_____
NAME
DATE
Test Chapter 10 (continued)
SCORE
ANSWERS
(See question)
20. Use a half-angle formula to find sin 75° without using
a calculator.
21. (See question)
21. Use a half-angle formula to find tan
a calculator.
750
without using
22.
22. a. Sketch y =2 sin 2x and y = .2 cos x on the same set of axes over
the interval 0 x < 2it.
(See graph)
(6)
(6)
(6)
(2)
22
(6)
24.
(6)
b. How many solutions do there appear to be in this interval?
23. Solve2sin2x=2cosforO.x<2it.
24 Solvesin2x=cos2xforOx<2it
* OPTIONAL
ANSWERS
1. Challenge Write cos 40 in terms of powers of cos 0 only.
2 WrIting Since calculators are readily available, why are the sum,
difference, half, and double-angle formulas important?
TESTSforADVANCED MATHEMATICS
—28
—
(See question)
2
•
ee question)
Copyright © by Houghton M(ftlin Company.
All rights reserved.
ca
answer.
DATE
of tinc.
Give the equation of the
following graph in terms
12.
-25-
x
Yl3CQI1r+J.
(
Solvecac 9=-ZI
9c6O°Lo the acgreattenih ofadegree.
Find the inc1iniop o(the line 4r-3y=1 to the nearest degre:
Tair’x.
(Sir’ ).
TF.STSIOrDvASIC1DUATHaSA71cS
14
cic
Give the domain and range o(y
13. Siipplify
5.
3.
10.
11.
7. Find the exact va1ic of
6. lftanx= - weOSx<ZKflndslnx.
5. Express cot 135° i termeofareference nglç.
• Shthegraphoy=IcosslfarOx<2K.
3. Ueisathadrantanglc.andsine=-j4fiMcose
CowjØete the feUowwg wh the best
1. Ezs-165°diaps;lcaveiniumsof*.
2. Fwdaofacersneorwitharckth6adcralaugle2
DkecUpnL Wi’iteanswe’s in
Cumulative Test Chapters 7—.
NAME
12
liz
•.
(continued)
4)
(4)
(4)
ci)
(4
(4)
(4)
.44 á1jaesqst
coiO
14
13.1.
(See graph)
y4ip2
11
1°;
•.________
••.
;.i!.
1.f
AW
scq
•
•
•
:1..
Uxncçst erec
&aIOhl5.fi1(tie
(4).thqre)
25. Al4ppiçe$O°fbrnesataapeedof12
b cechan,soaçrag tip
fcr2moçebours. Bow (arts
106.3°
in.
nLItmi
2167km
23.36
20.
-or143°
is. iOD.. ft
17.
ir5z3z.
15. (See guest on)
(4)
(4)
(4)
(4)
(4)
(4)
(4)
(4)
(4)
(4)
GRE_
Cpy
g
4
k( Cky Jdo,gbwe ia’ijzu c,
A1.igkiimeøwS
thcac,
magonlnscc4bed’
mra4s6mcta.
24. Aa
llcecofladoflOIun1h How
fvcaq&n taitmpcqiL nell g be after 2 bows? (kound so the
3.
4,
•
Iterntsolz.
PATE
SRI
wdkpdcWofS° WwCenthC
sqaznd die pop o’ Øe gmua4ddy below the auplane?
2ia
x
2
i.aine-1=Q
4aox—3secx
e1ar$x<2!4e.wauranl
Gjveq b. 4itgr*i qd°r
4*.
15.
AM
DATE
750
2
in simplest radical form.
ac
14. cos 4a
()
—
2
sin
()
TF.S7’SforADVANCED MATHFJ4A77S
l+cos2x
18. 2cos
(3A)—l
2
17. cos
2
Simplify.
15. an2
16.
-27-
tan3
If tan fl= ,evaluate the following without using tables era calculator.
13. cos 2a
and sin a=, evaluate the following without using tables
or a calculator.
12. sin 2a
110
4V
9
—
1. tefl
x
cos6A
14.
X
99
-5
17
81
15
7
17. COS
IS.
14.
13.
12.
(4)
(4)
(4)
(4)
(4)
(4)
(4)
(4)
(4)
(4)
4)
(3)
(3)
(3)
(3)
(3)
(3)
(3)
(continued)
AO. 4’5O
11. ‘ “
10.
cos x
7
—
slny
4.
sometimes
always
4.
never
lwa
2.
sometImes
ANSWERS
SCORE
Copyright C by Hoogkso.i ltØIIo Cow,y
AS rights ,,wwS
10. Usc a awn or difference formula to find tan 3450 in simplest radical form.
11. Findthetwosupplementaryanglesbetwceny=2x+3andy=1 -3x.
4’
9. Evaluate tan (!_x’ iftanxsi-.
g. cos(+x)+cos(x)
7. sinxcos(x+y)—cosxsin(x+y)
Simplify.
6. Use a sum formula to find sin
Solve.
4. When you use the half-angle formulas, you choose whether to use +
or- by noting in which quadrant the angle lies.
5. Using a graphing utility (or graphing calculator) to solve a system of
tzigonometric equations yields exact results.
3. lftana=3andtanfl=2,thenlan(a+fl)=5.
2.cos(+8)=.sin8
Clawify each oldie following as always, soniedmes, or never true.
1. sin 2x=2sinx
Dliwctlons: Write answers ii the spaces pmvided.
Test Chapter 10
NAME
0
2
without using
2+Vor\/=V7+4V
DATE
TES7SforADVANCED MATHEMATKS
practice).
-25-
4
it
it
graph)
(2)
(6)
(6)
(6)
2.
1.
(See question)
(Sec question)
ANSWERS
5it 3it
.L T 2 (6)
22
it Sit Sit l3it
24. ‘T’ 8’
(6)
22.
“°°
(See question)
ANSWERS
SCORE
_____
Copyright C by Hoiigt.to., Mifflu’ Co..,po.ey.
All rights reserw
Answers may vary.
These Identities allow one to simplify complicated
expressions. They also yield exact answers (even
though calculator approximations are good in
2. IeWtlng Since calculators are readily available, why are the sum,
difference, half, and double-angle formulas important?
2
Scos’8—8co
8
+1
s
1. CbaIlonpWnte cos 401n terms of powers of cos 8 only.
*. OFIIONAL
23. Solve2sin2x=2cosxfar0x<2t.
24. Solvesin2x=cos2rforOx<2,r.
b. How many solutions do there appear to be in this interval?
22. a. Sketchy=2sin2xandy=2cosxonthesamesetofaxesover
the interval 0 x < 2x.
a calculator.
•
750
21. Use a half-angle formula to find tan 75° without using
•
20. Use a half.angle formula to find sin
a calculator.
Test Chapter 10 (continued)
NAU
__
NAME
DATE
SCORE
1 —11
7—11
Cumulative Test Chapters
Part
II:
Test Chapters
Directions: Write the letter of the correct answer in the space provided.
1. Convert 34°57’ to radians.
Give the answer to the nearest
hundredth of a radian.
a.
b.
c.
d.
e.
ANSWERS
3. If the terminal ray of 0 passes
through (—4, 5), find cos 0.
a.
34.57
34.95
0.61
2002.49
None of these
b
(3)
2.
(3)
3.
(3)
4.
(3)
5.
(3)
6.
(3)
7.
(3)
8.
(3)
VT
•
d
1.
vr
e. None of these
4. Express cos (— 128°) in terms of
its reference angle.
a. cos 232°
b. cos (—38°)
c. —cos 38°
d. —cos 52°
e. None of these
2. A circular sector has a radius
of 9 and a central angle of 2
radians. Find the arc length.
a.18
I..
5. Simplify cot (x + it).
a. cotx
b. —cot x
C. tanx
d.
e. None of these
U
10
c. 9ic
d.
e. None of these
6. Which graph below represents y.
=
Siir’ x?
a.
d.
C.
2::IE:I:
,,
:jh:
0
o
5
L
‘,
e. None of these
7. How many solutions are there to
2 x =25 (0 x < 2it)?
csc
a. 1
b. 2
c. 3
d. 4
e. None of these
8. Find the equation ofa line with incli
nation 45° that passes through (1,4).
a.
b.
c.
d.
e.
y—4=45(x—1)
y—4=x--1
y+4=\/(x+1)
y+4=x+1
None of these
(continued)
TESTS for ADVANCED MATHEMATICS
—36—
Copyright © by Houghton Muffin Company.
All rights reserved.
SCORE
NAME
DATE
Cumulative Test 1 —11 • Part ii: Chapters 7 —11
(continued)
11111
10.
d.
e. None of these
a.. y_2=Asin,-!!(x_3)
•
-
(3)
11.
_(3)
12
(3)
13_______ (4).
tE
=Asinis
1
Ifthegraphofy
10 x
translated 3 units to the right and’.
2unitsup,thçn
(3)
9.
9. Which of the following is the graph of y 3 sin 2x?
b.
a.
C.
ANSWERS
14.
(4)’
15.
(4)
16.
(3)’
13 Solve
3sinx=5 sin x +2(0 x < 2i)..
b. 4.71
a. 5.94
d. 5.94;. 3.48
c. 3.48
e. None of these
b. y+2=Asm!!(x+3)
c. y_3=Asin.-!(x_2)
d....y+3=Asin!!(x+2)
e. None of these
11. Which of the following is true?
a. sin 9=cos(90°+0)
b. cot(—6)=cot0
9=l
2
2 9+cot
c. tan
=1
0+sec
csc
9
d. 2
e. None of these
49
4 9— co
sin
12. Simplify 2
z
sin 9— 2
29
2 0— cos
a. sin
‘a
d. —1
e. None of these
14 Find the perimeter of an isos’
celes triangle with a base of 8
and a vertex angle of 200.
b 1O0
a... l9..
de,24:
c.- 54
e. Nóneofthese
1& A regular octagon with sides of.
length 6 is inscribed in a circle..
Find the area of the octagon.
b. 174
a. 48
d. 11
c.22
e None of these
16. Find the radius of the circle in
Exercise 15.
b. 1.1
a. 7.8
d. 8.5
c. 6.0
e. None of these
(continued)
TESTSfor ADVANCED MATHEMATiCS
—37—
Copyright @ by Houghton Muffin Company.
All rights reserved.
_____
___
_____
NAME
DATE
Cumulative Test 1 —11
•
Part II: Chapters 7— 11 (continued)
17. Find the measure of the largest
angle in a triangle with sides 3,
6, and 7.
a.
b.
c.
d.
e.
SCORE
22. Which of the following is equal
to cot 75°?
1—tan45°tan30°
a
tan 45° + tan 30°
l+tan45°tan30°
b
tan45°—tan30°
tan 45° + tan 30°
C.
I—tan45°tan30°
86.8°
83.6°
96.4°
96.4° or 83.6°
None of these
d
I+tan45°tan30°.
e. None of these
18. In AABC, LA = 30°, a = 10 and
b= 10V. Find LB.
a. 45°
b. 135°
C. 115°
d. 45° or 135°
e. None of these
(
23. If sin a =
sin 2cr.
a.it
and cos
13=44
<it,
b 176
185
46
185
,1
“
(3)
19.
(3)
20.
(4)
21.
(3)
22.
(4)
23.
(3)
24.
(3)
25.
(3)
26.
(4)
x < 2it
25. Simplify the expression
1+cos48
sin 48
•
a. cot 88
b. 1 + cot 48
c. tan2O
d. cot28
e. None of these
‘
find
cos(a÷J3).
a.
18.
5
bit
c. all x such that 0
5it 9it l3it
d
8’ 8’ 8’ 8
e. None of these
20. Find the acute angle between the
linesy=4x+2andy=7—3x.
a 325°
b 531°
c. 36.9°
.d. 0.6°
e. None of these
(4)
24. Solve sin 2x = cos 2x over
0 x < 2ic.
c.
<13
fmd
17.
c
2
e. None of these
a. 034°
b. 011°
169°
d. 326°
e. None of these
and 0< a <
<,
a
a. 1
19. A ship leaves port and sails for 2
hours northeast and then 3 hours
northwest. If the speed remains
constant, what course should the
ship take home?
21. If sin a =
and 0 <
ANSWERS
185
e. None of these
TESTSfor ADVANCED MATHEMATICS
26. Which polar equation describes
the graph?
a. r=sin28
b. r=cos28
c. r=cos49
d. r=sin48
e. None of these
it
(continued)
-38-
Copyright © by Houghton Muffin Company.
All rights reserved.
ANSWERS
l.C
(3)
(3)
,b
3
(3)
d
(3)
&a.
(3)
(3)
d.
(3)
(3)
(3)
(3)
(3)
(3)
13.
d
(4)
(4)
14.
(4)
(3)
17. C
(4)
1L
(3)
(3)
(4)
(3)
a
(4)
(3)
d
(3)
d
(3)
24.
(4)
C