Download Math142 PracticeQuestionsforMT3

A) 0.9372
B)
A)
B) -0.9372
4
4
3
5
A)
B)
C)
3
10) sin-1 sin
4
4
4
5
21) cos-1 cos
3
10
2) cos-1
22
3
-1Test
Practice
2
A)
B)
5) sinfor
(0.5)
5
A)
B) 10 5
C) - 11
10
10
7
7
A)
B)
A) Find the
exact
value
of
the
expression
A)
B)6
C) 6
6
6
3
a.
b.
4
11) tan-1 tan
22) sin-1 sin
5
3 Secant, Cosecant, and Cotangent Functio
2 Define the
Inverse
5
3
-1
3) cos
6) tan-1
4
3
A) - 2
B)
A)
B)CHOICE.
5 5
- 5
MULTIPLE
Choose the oneC)alternative
that best comp
5
55
7
c.
d. A)
B)
A)
B)
C)
66
6
3
Find the exact 6value
of the expression.
3
12)
-1-1-115)sec
cotsin
23) tan-1 tan 2
8 Value
Define
Inverse Secant,
Cosecant,
Cotangent
22 Find
anthe
Approximate
of an
Inverse
Cosine, or Tangent Function
-1 (1)Sine,
4)and
tan
3 Functions
A)
B)
3or answers
4
4
A)
2
B)
1
MULTIPLE
CHOICE.
Choose
the
one
alternative
that
best
completes
the
statement
the question.
A)
B)
C)
8
e.
MULTIPLE
CHOICE.
Choose the onef. alternative
that best completes the
or
answers th
A) 8
B) statement
8
4
4
Find the exact value of the expression.
Use a calculator
to find the value of 16)
the csc
expression
-1 - 2 rounded to two decimal places.
-1 -1
4 Find 15)
thecot
Inverse
Function
of
a
Trigonometric
3
-1Function
7) sin-13(-0.3)
13)
sec-1tan
5) sin
(0.5)
2
3
B) f A) C)
D)
B)
-1 of the function
B) FindA)
the
inverse
function
f
A)
B)
C)
1.88
-0.30
-17.46
4
4
7 4 or answers 3the q
MULTIPLE CHOICE.
Choose the one alternative
that
4 best completes3the statement
A) 2 3
B)
a. f(x) =2 sin x – 5
A) 6
B) 2 6
b.cos
f(x)
=7
tan 8x f-1 of the function f. 3
-1
-1
Find the16)
inverse
function
8)
(0.3)
csc
- 2
c. f(x) = cos(x-6) – 7
17) sec -1 1
24) f(x) A)
21.27
sin x - 5
=
B) 72.54
C) 0.30
A) B)
C)
D)
3
C) Find the domain
of f and f-1x + 5 6) tan4-1
4
3
6
x
5
+
A)
0
B)
2
B) f-1 (x) = cos
A) f-1 (x) = sin-1
-1
3
14)
tan
sin
-1=(2.3)
2
2
f(x)
-5cos(9x)
9)a.tan
2
-1
b.
f(x)
=
5sin(8x-1)
17) secA) 1.16
1
C)
A)B) 66.50
B)
c. C)
f(x)f-1
= tan(x-3)
+ 6-1 x + 2
-10.41
-1 - 5
(x) = sin
D)
f
6
-1
A) 1 (-2)
B) 3(x)
2 = 2 sin x D)
18)
5
A) 0
B) sec
C)
6
3
D) Find the exact solution of the equation
2
B) A)
!
-1(4x) =
2 Find an Approximate
Value of an Inverse Sine,
a. –sin
3 Cosine, or Tang
3
25) f(x)
7
cos
x
6
=
+
!
18)b.sec2-1
(-2)
-1
cos x = 𝜋
Page 602
x-6
x-6
-1
2
2 -1(x)
c. A)
-4 tan
x ==
𝜋 cos-1MULTIPLE CHOICE. Choose the one4 alternative
B) f-1 (x) =that
sin best complete
f
B)
C)
D) A)
7
7
3 Use a Calculator
to Evaluate sec^-1
x, csc^-1 x, andPage
cot^-1
3
3
3x
3
610
E)
x +a6calculator to find the value of the expression
rounded
-1 x + 6to two
C) f-1 (x) = cos-1Use
f-1 (x) = 7 cos
MULTIPLE
CHOICE.
Choose
the oneD)alternative
that best
comp
3 Use a Calculator to Evaluate sec^-1
x, csc^-1
x,
and
cot^-1
x
7
Copyright © 2011 Pearson Education, Inc.
7) sin-1 (-0.3)
4) tan-1 (1)
MULTIPLE CHOICE. Choose the
oneaalternative
that
completes
the statement
or answers the
question.m
A) -0.30
-17.46
Use
calculator
tobest
find
the value
of theB)expression
in radian
Copyright © 2011 Pearson E
26) f(x) = 7 tan(8x)
7
-1 in radian measure rounded to two decimal
Use a calculator to find the
of the expression
places.
csc
1 value
-1 x 8)19)
-1 (x) = 1 tan-1 x
-1
tan
B)
f
A) f-1
(x)
=
4
cos
(0.3)
7
7
8
7
8
19) csc-1
4
1
-1 (x) =
C)
A) f0.61
7 tan(8x)
20) sec -1 - 8
27) f(x)A)
= -8
1.70cos(3x)
x
1
A) f-1 (x)
= cos-1
5
8
3
21) cot-1 -
A)A)
1.27
0.61
B) 34.85
-1-1
(2.3)
9)20)
tansec
-8
A)A)
1.16
1.70
B) 97.18
5
21) cot-1 14
14
x
1
-1
-1
C)
(x) = - cos
A) f-1.23
B) -70.35
A) -1.23
8
3
B) 72.54
B) 34.85
C) 0.96D) f-1 (x) = 7 tan-1 (8x)
D) 55.15
C) -0.13
B) 66.50
B) 97.18
D) -7.18
x
1
B) f-1 (x) = cos-1
3
8
D) f-1 (x) = -8 cos-1Page
(3x)
602
C) -0.34
D) -19.65
B) -70.35
sindepth
sinis rin
below
the
surface
of
of the
andfrom
S is
theexample,
total horizontal
i = n r(also
where
M
thekilometers)
horizontal
movement
(in meters)
atcenter
arepresented
distance
d earthquake,
(in
earthquake,
D is the
75)niThe
seasonal
variation
in the length
of daylight
canthe
be
by akilometers)
sine function.
For
the daily
Solving for
,
we
obtain
kilometers
from an
displacement
in meters)
at the
line.
is theofhorizontal
movement
r (also in (also
depth
kilometers)
below
thefault
surface
ofWhat
the center
the earthquake,
the
41and5 S5 is
2 xtotal horizontal
number of hours of daylight in a certain city in the U.S. can be given by h =
+
sin
, where x is the
n
earthquake
centered 3 kilometers below the surface with a total horizontal4displacement
meters?
an Round
displacement
3 5 kilometers
365 of 4 from
-1 i sin i (also in meters) at the fault line. What is the horizontal movement
r = sin
nr
the
answer
to
the nearest
0.01 meter.
earthquake
centered
3 kilometers
below the surface with a total horizontal displacement of 4 meters? Round
number of days after March 21 ( disregarding leap year). On what day(s) will there be about 10 hours of
the answer to the nearest 0.01 meter.
Find daylight?
r for crown glass (n i = 1.52), water(n r = 1.33), and i = 38°.
75) The seasonal variation in the length of daylight can be represented by a sine function. For example, the daily
6.4
74) The ground movement of an earthquake near a fault line is modeled by the equation
75) The seasonal variation
in the length of daylight can be represented by a sine function.
the daily
41 5 For
2 example,
x
2M
, where x is the
number
hours
d = D tanof Identities
1 - of daylight in a certain city in the U.S. can be given by h =
+ sin
Trigonometric
41
5
2
x
2
S
4
3
365
, where x is the
number of hours of daylight in a certain city in the U.S. can be given by h =
+ sin
4
3
365
where M is the horizontal movement (in meters) at a distance d (in kilometers) from the earthquake,
D
is the
number
of daysTrigonometric
after March 21Expressions
( disregarding leap year). On what day(s) will there be about
10 hours of
1 Use Algebra
to
Simplify
depth (also in kilometers) below the surface of the center of the earthquake, and S is the total horizontal
number of days after March 21 ( disregarding leap year). On what day(s) will there be about 10 hours of
daylight?
displacement (also in meters) at the fault line. What is the horizontal movement 5 kilometers from an
daylight?
SHORT ANSWER.
Write
the 3word
or phrase
completes
each
statement
or answers
question.
earthquake
centered
kilometers
belowthat
the best
surface
with a total
horizontal
displacement
ofthe
4 meters?
Round
the answer to the nearest 0.01 meter.
6.4 Trigonometric
Identities
Simplify
the trigonometricIdentities
expression by following the indicated direction.
6.4 Trigonometric
75)
The
seasonal
variation
in the
length
of daylight
canxbe represented by a sine function. For example, the daily
1) Rewrite
of sine
and
cosine:
tan
x · cot
1 Use
Algebrain
toterms
Simplify
Trigonometric
Expressions
41 5
2 x
1 Use number
Algebraofto
Simplify
Trigonometric
Expressions
in the U.S. can be given by h =
sin
, where x is the
hours
of daylight
in a certain city
+
4
3
365
SHORTnumber
ANSWER.
Write
the
or
phrase thatleap
bestyear).
completes
each statement
or answers
the question.
1word
cos(or
sin
+ 21
of days
afterthe
March
disregarding
On what day(s)
will there
about 10 hours
of
SHORT
ANSWER.
Write
word
phrase that
best
completes
statement
orbeanswers
question.
2) Multiply
49)
When
light
travels from
oneby
medium
to another
from
air to
water, foreach
instance
it changes
direction.the
(This
is
daylight? 1 - cos
1
cos
+
F) aWrite
trigonometric
expression
as an
in u: of incidence r is the angle in
why
pencil,
partially
submerged
in water,
asalgebraic
though
isexpression
bent.) The
angle
Simplify
the the
trigonometric
expression
bylooks
following
theitindicated
direction.
Simplify
thesin
trigonometric
expression by following the indicated direction.
-1u)
a.
(cot
the
first
medium;
the
angle
of
refraction
is
the
second
medium.
(See
illustration.)
Each medium has an index
1) Rewrite inIdentities
terms of sine and cosine:
tan x · cot x
6.4 Trigonometric
r
1)
Rewrite
in-1u)
terms of sine and cosine:
tan1x · cot x 1
b.
cos
(csc
of refraction
nover
, respectively
which can be found in
i and-1an rcommon
Rewrite
denominator:
+ tables. Snell s law relates these quantities in the
1 Use 3)
Algebra
to Simplify
Expressions
c. tan
(sec u) Trigonometric
1 - sin
1 + sin
formula
1
cos
sin
+
1
cos
sin
+
by
2)
Multiply
SHORT ANSWER.
wordby
or phrase that best completes each statement or answers the question.
sinMultiply
sin 1 the
i 2)
i = nWrite
rthe
11 ++ cos
cos using the directions provided:
G)nSimplify
following
1 r-- cos
cos expressions
Solving
for
,
we
obtain
(tanby following
+ 1)(tan the
+ 1)indicated
- sec 2 direction.
Simplify the trigonometric
expression
r
4)
Multiply and simplify:
1) Rewrite innterms
of
sine
and
cosine:
tan
x
cot
x
tan·
i
11
11
sin
= sin-1
r3)
3) Rewrite
Rewrite
over iaa common
common denominator:
denominator: 1 - sin ++ 1 + sin
n r over
1 - sin
1 + sin
1 + cos
sin
by
2) Multiply
Find r for air (n
1.0003), methylene
16+sin
cos2 +iodide
1 i-=cos
7 sin (n+r =1 1.74), and i = 14.7°.
5) Factor and simplify:
2 -++ 11)(tan ++ 1) -- sec22
(tan
sin
1
1
4) Multiply and simplify:
3) Rewrite over a common denominator:
+
1 - tan
sin
1 + sin
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
2
(tan6 sin
1) - sec
+ 1)(tan
2 + 7 +sin
+1
4) Multiply and simplify:
5) expression.
Factor and simplify:
tan
Simplify the
sin2 - 1
cos
6)
+ tan
1 + sinand simplify: 6 sin2 + 7 sin + 1
5) Factor
alternative that best completes the statement or
sin2one
-1
MULTIPLE CHOICE. Choose the
or answers
answers the
the question.
question.
A) sec the expression:
B) cos + sin
C) 1
D) sin2
H) Simplify
Simplify
the expression.
expression.
MULTIPLE
Choose the one alternative that best completes the statement or answers the question.
Simplify
the
a. CHOICE.
cos
cos
7)
(1
cot
)(1
+
tan ) - csc2
6) expression.-++ cot
Simplify the
tan
6)
1 ++ sin
sin
1
cos
2
A) -2 cot
B) 0
C) 2
D) 2 cot2
6)
+ tan
1 + sinA) sec
2
B)
cos
sin
C)
1
D)
+
A) sec
B) cos + sin
C) 1
D) sin
sin2
2
A)
sec
B) cos + sin
C) 1
D) sin
b.
2 Establish
Identities
7) (1 + cot )(1 - cot ) - csc2
2
7)+(1
cot
+ cot
(1
cot
)(1
cot) - csc)2- csc
- )(1
SHORT 7)
ANSWER.
Write
that
each statement
the question.
2the word or phrase B)
A)
cot
0 best completes C)
C) 2 or answersD)
D) 2 cot22
-2
2 cot2
A) -2
cot
B) 0 B) 0
2
2 cot2
A)
C)
2
D) 2 cot
-2
G) Establish the following identities
Establish the identity.
Establish
Identities
2 2Establish
Identities
2 Establish
Identities
8) (sin x)(tan
x cos x - cot x cos x) = 1 - 2 cos 2 x
Page
608
SHORT
ANSWER.
Write
the word
or phrase
that best
completes
each statement
or answersor
theanswers
question.the question.
SHORT
ANSWER.
Write
the word
or phrase
that
best completes
each statement
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Establish the identity.
Establish
identity.
3the
2x cos
2 xx)-=cos
28)
x cos
x = xsin
x (cos
1 -42x)
cos 2 x
8) sin
(sinthe
x)(tan
x cos
- cot
Page 621
Establish
identity.
Inc.
1 - Pearson
2 cos 2Education,
x
8) (sin x)(tan x cos x - cot Copyright
x cos x)©=2011
8) (sin x)(tan x cos x - cot x cos x) = 1 - 2 cos 2 x
29) csc3 x tan2 x = csc x (1 + tan2 x)
Page 621
H) Complete the follwing identities (multiple choice).
Page 621
Copyright © 2011 Pearson
Education, Inc.
1.
30) cot x sec 4 x = cot x + 2 tan x + tan3 x
Page 621
Copyright © 2011 Pearson Education, Inc.
sin x
sin x
31)
+
= 2 tan 2 x
csc x - 1 csc x + 1
2.
32)
cos x
2 cos x
cos x
=
sec x - 1 sec x + 1 tan2 x
33)
1 - 2 sec x - 3 sec 2 x 1 - 3 sec x
=
2
1 - sec x
Copyright © 2011 Pearson Education, Inc.
Copyright © 2011 Pearson Education, Inc.
3.
4.
5.
6.
I)
Use sum and difference formulas to fin exact values of the following expressions:
a. cos 285°
!!
b. tan
c.
d.
!"
!!!
sin−
!"
!!!"# !"°!"#!"°
!"# !"°!!"#$!°
J) Find the exact values under the specified conditions
a.
b.
c.
K) Establish the following identities using sum and difference formulae.
5
4
59) cos tan-1
- cos-1
12
5
A)
63
65
B)
13
24
C)
7
13
D)
52
65
Write the trigonometric expression as an algebraic expression containing u and v.
60) cos (sin-1 u - cos-1 v)
L) Complete the following
2 identities using
2 sum and difference formulae.
A) v 1 - 5u + u 1 -4v
59) cos tan-1
- cos-1
C) uv - ( 121 - u2 )( 15 - v2 )
63
-1
-1
61) cosA)
(tan
65 u + tan v)
B)
13
24
B) v 1 - u2 - u 1 - v2
D) uv + ( 1 - u2 )( 1 - v2 )
C)
7
13
D)
5
4
1 + uv
u2 + 1 · v2 + 1
59) cosA)tan-1 1 - -uvcos-1
B)
C)
D)
12
5
1
uv
2
2
2
2
v
1
v
1
u
1
u
1
·
+
·
+
+
+
Write the trigonometric expression as an algebraic expression containing u and v.
63
13
7
B)
C)
60) cosA)(sin-1 u - cos-1 v)
65-1
24
13
62) sinA)
(tan
2 + -1
v 1 u- +utan
u v)1 - v2
B) v 1 - u2 - u 1 - v2
1 + uv containing u and v. u2 + 1 · v22+ 1
u + vexpressions
M) Write the trigonometric
as2algebraic expressions
C) uv - ( 1 expression
1 -v.u )( 1 - v2 )D)
- u2 )( 1 - v
C)D) uv +u (and
A)
Write the trigonometric
as)anB)algebraic expression containing
u +1· v +1
u +1· v +1
60) cos (sin-1 u - cos-1 v)
1.
-1 u + tan-1 v)
2.61) cos (tan
2 u 1 - v2
A)
v
-11u--utan+-1
63)
sin
(tan
v)
3.
1 + uv
1 - uv 2
A) uv - ( u 1- -v u )( 1 - v2 ) B)
C)
1
- uv
N) Solve theA)
following
0u2
≤θ<2𝜋
B)
v2 + 1 on the interval
u2 +trig
1 ·equations
+ 1 · v2 + 1
2
2
u2 + 1 ·
v2 + 1
u2 + 1 ·
v2 + 1
!
,0 < 𝜃 <
!
u
B) v 1 - u2 - u 1 - v2
u2 + 1 · v2 +2 1
C)D)uuv
)
2 + +1 (· 1v2- +u1 )( 1 - v2D)
1 - uv
C)
D)
1 - uv
-1=u0+ tan-1 v)
1.
𝑐𝑜𝑠𝜃
61) 𝑠𝑖𝑛𝜃
cos +(tan
2.62)𝑠𝑖𝑛𝜃
=
𝑐𝑜𝑠𝜃
-1 u + tan-1 v)
sin (tan-1
-1 v)
1 + uv
u2 + 1 · v2 + 1
uv
64) cos
(sin
u 1+= cos
3.
3𝑠𝑖𝑛𝜃
− 𝑐𝑜𝑠𝜃
−1
B)
C) 2
A)
v2 + 12
u +211· - uv
2+1
2 1+ +1uv
2-+uu12+·-vuv21 +- 1v2
A)
v
1
B)
v
1
u
u
1-v
+
v
u
u
·
B)
C)
A)
O) Use the information given about the angle to 𝜃, 0 ≤ 𝜃 ≤ 2𝜋, to find the exact value of the
1 - uv
2
2
2
2 + 1functions.
v
1
v
1
u
1
u
·
+
·
+
+
indicated trigonometric
C) uv - ( 1 - u2 )( 1 - v2 )
D) uv + ( 1 - u2 )( 1 - v2 )
1. 𝑠𝑖𝑛𝜃 =
D
1 - uv
2
2
u
u
D
D)
, find cos 2θ.
62) sin (tan-1 !u!!+ tan-1 v)
2.
𝑡𝑎𝑛𝜃
, 𝜋 < 𝜃 < , Equations
find-1
sin 2θ. Linear in Sine and Cosine
4 Solve
Trigonometric
!" (tan-1 u! - tan
63)=
sin
v)
1 + uv
u2 + 1 · v2 + 1
u+v
B)
C)
A)
2
P)
Solve
the
problem
v2 + 1 the questioD
1 -best
uv completes the statement
u + 1or
u - v the one alternative that
· -answers
MULTIPLE CHOICE.
Choose
1
uv
2
2
B)
C)
D)
A)! u2 + 1 · v2 + 1
u find
+ 1sin· 2θ.v + 1
1. If sin θ = − , and2θ terminates
in Quadrant IV, then
1
uv
2
2
2
!
v +1 0
u +1· v +1
uon+ the
1 · interval
!
Solve the equation
<2 .
!"
!"
2. If tan θ = −
!"
, and θ terminates in Quadrant III, then find cos 2θ.
0 -1
+ sin
-1 u -= tan
63) sin (tan
v)
-1
7u + cos-1 v)
3
64) cosA)(sin
, u-v
4 2
4
A)
65) cos
A) v 1 - u - u 1 - v2
u2 + 1 · v2 + 1
C)
uv
- ( 1 - u2 )( 1 - v2 )
66) cos = sin
5
3
B)4
B)
1 - uv
u2 + 1 ·
7
v2 + 1
3
2
C)
u2 + 1 · v2 + 1 D) - 6
D
B) v 1 - u2 + u 1 - v2
1 - uv
D) uv + ( 1 - u2 )( 1 - v2 )
C)
3
5
3
,
,
C)
,
D)
-1
-1 v) LinearB)in Sine
64)Trigonometric
cosA)(sin
4 Solve
Equations
4 4u + cos
4 4 and Cosine
4
4
4
2
2
2
2
A) v 1 - u - u 1 - v
B) v 1 - u + u 1 - v
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the ques
20) If cos 2 = A)
24
, and
< 2 < , then find sin .
25
2
7 2
10
B) -
7 2
10
C)
7
5
D) -
7
5
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Q)
21) The path of a projectile fired at an inclination
(in degrees) to the horizontal with an initial speed v0 is a
parabola. The range R of the projectile, that is, the horizontal distance that the projectile travels, is found by
using the formula
2
v0
R=
sin (2 )
g
where g is the acceleration due to gravity. The maximum height H of the projectile is
2
v0
H=
4g
(1 - cos (2 ))
Find the range R and the maximum height H in terms of g if the projectile is fired with an initial speed of 200
meters per second at an angle of 15° and then at an angle of 22.5 °. Do not use a calculator, but simplify the
answers.
R) Use the information
given about
the angle to 𝜃, 0 ≤ 𝜃 ≤ 2𝜋, to find the exact value of the
2 Use Double-angle
Formulas to Establish
Identities
indicated trigonometric functions (use half angle formulae).
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
!
1. 𝑠𝑖𝑛𝜃 = , 0 < 𝜃 <
!
!
, find sin .
!
!
!
Establish the identity.
!!
!
, 𝜋2u)
≤ 𝜃
, find
2 u (1=+3cos
22) 2.
tan𝑡𝑎𝑛𝜃
2u tan .
= 1≤- cos
!
!
S) The polar
coordinates of a point are given. Find the rectangular coordinates of the point.
1
23) a.
cos4 x =
8
( 3 + 4 cos 2x + cos 4x)
2
21) -3,
The letters
r and represent
polar coordinates. Write the equation using rectangular coordinates (x, y).
24) cos 3x 3
= cos3 x - 3 sin2 x cos x
46) r = cos
3 -3 3
3 3 3
3 3 3
-3
b. (-3,
-135
°) 3x
232,+sin
A)
y 22u= cos
B) x-2 + ,y 2 = y
C) (x ,+ y)2 = x
D) (x
A)
C)
D)
- + ,y)2 = y
25) c.
sin(-3,
4u x
2u
=
45°)
2
2
2
2
2
2
2
2
47)T)
r =The
1 +=rectangular
2(4sin
26)
sin
4x
sin x cos x)(1
- 2 sin2 x) of a point are given. Find polar coordinates for the point.
coordinates
32
(8,
22)a.-5,
A) 0)
x + y2 = x2 + y2 + 2y
B) x2 + y2 = x2 + y2 + 2x
4
b. ( 3, −1)
1 + y2
The letters
represent
coordinates. Write the equation
coordinates (x, y).
y26x)
2y
D) x2 + y2using
y2 + 2x
= x2-+cos
+polar
= x2 + rectangular
27) sin3C)r3xand
3x)(1
=x2 (sin
5 2 2 -5 2
5 2 5 2
-5 2 5 2
-5 2 -5 2
46) rA)= cos ,
B)
,
C)
,
D)
,
U) The letters x and y represent rectangular
coordinates.
Write the2equation
2
2
2 using polar
2
2
48) r = 10 sin2 2 2 2
2
2
2
A) x (r,
y =x
B) x + y = y
C) (x + y) = x
D) (x + y)
+ θ).
coordinates
2 + y 2 = 10x
2 + y2 = 10y
2 + y2 = 10x
2 x2 +2y 2 = 10y
A)
B)
x
C)
x
D)
x
a. x3 + y - 4x = 0
Page 634
23) 3, 2
47)
r=
14y
sin4
+ 22 =
b.
x
+
4
49) r = 2(sin - cos )
c. xy
=1
22-=2x x2 + y2 B)
22++2y2y
2-3
3 2 2 -3
2 B)
2
-3
2 2
2+ 2x
x2 + y2 =D)
+ 2y
A) A)
x2-3+xy222+=3y2y
C) x32 +2y, 23= 2x
D) x2x
- 2y
B) 2x + ,2y = y - x
C)
, =x-y
d. yA)
=5 2 , 2
2
2
2
2
2
2
C) x2 + y2 = x2 + y2 Copyright
D) x2 + y2 = x2 + y2 + 2x
+ 2y © 2011 Pearson Education, Inc.
50)V)
r =The
5 letters r and θ represent polar coordinates. Write the equation using rectangular
4x2 + y 2(x,
D) x + y = 5
25
B) x2 - y 2 = 25
C) x + y = 25
= y).
coordinates
24)
5,A)
48)
r-= 310 sin
a.
2
2
2
2
5 5x25+ 3y 2 = 10y
D) x2 +
5 B)
5 x
3 + y = 10x
5 3 5 C) x + y = 10y
5 3
5
51) r =A) A)
,
B)
,
C)
,
D)
,
1 + cos
2
2
2
2
2
2
2
2
2
49)
r 2(sin
- cos )
B) y2 = 10x - 25
C) x2 = 25 - 10y
D) x2 = 10y - 25
b. A)=y = 25 - 10x
25) (-7, 120°)
A) x2 + y 2 = 2y - 2x
B) 2x2 + 2y2 = y - x
C) x2 + y 2 = 2x - 2y
52) r sin 7= 10
-7 3
A) y =, 10
A)
2
2
50) r = 5
7 -7 3
B) x-= 10
,
B)
2
2
53) r(1 - 2A)
cosx2)+= y12 = 25
26) (-3, -135°)
A) x2 + y2 = 1 + 2x
3 2 3 2
A)
5, 2
51) r = 2
B) x2 + y 2 = 1 + 2x
3 2 -3 2
B)
,
2
2
27) (5, 270°)
A) y2 = 25 - 10x
A) (0, -5)
B) (-5, 0)
1 + cos
7 7 3
C)
C) y2=, 10x
2
C) x + y = 25
B) x2 - y 2 = 25
B) y2 = 10x - 25
C) x2 + y2 = 2 + x
-3 2 -3 2
C)
,
2
2
C) (0, 5)
D) 2x2 +
7 7 3
D)
,
D) x- =2 10y
2
D) x + y =
D) x2 + y 2 = 2 + x
-3 2 3 2
D)
,
2
2
C) x2 = 25 - 10y
D) (5, 0)
D) x2 = 1