(aqt73) to Drill 9 seckin (54330)
1
This print-out should have 41 questions.
Multiple-choice questions may continue on
the next column or page nd all choices
before answering.
Explanation:
001 (part 1 of 4) 10.0 points
Suppose
003 (part 3 of 4) 10.0 points
c) Find sec .
5
csc = ,
4
a) Find sin .
1.
2.
3.
4.
5.
tan =
4
3
5
4
4
3
3
4
3
5
5
3
cos =
5
correct
3
4
2.
5
5
3.
4
1.
4. None of these
3
5
4
6.
3
3
7.
4
Explanation:
5.
6. None of these
4
correct
5
Explanation:
is in Quadrant I.
7.
1
4
sin =
=
csc
5
002 (part 2 of 4) 10.0 points
b) Find cos .
1. None of these
2.
3.
4.
5.
6.
7.
sin
43
3
==
tan
54
5
5
3
4
3
3
correct
5
5
4
4
5
3
4
sec =
5
1
=
cos
3
004 (part 4 of 4) 10.0 points
d) Find cot .
1.
2.
3.
4.
5.
6.
4
5
5
3
5
4
3
correct
4
3
5
4
3
7. None of these
Explanation:
cot =
3
1
=
tan
4
to (aqt73) Drill 9 seckin (54330)
005 (part 1 of 4) 10.0 points
Suppose
5
cot = 2, sin =
5
a) Find cos .
5
1.
2
2. None of these
25
correct
3.
5
1
4.
2
5. 5
2
1. 2
5
2.
2
1
3.
2
25
4.
5
5. 5 correct
6. None of these
Explanation:
5
5
1
= = 5
csc =
sin
5
5
6. 2
Explanation:
is in Quandrant II.
sin
25
cos
= cot sin =
sin
5
006 (part 2 of 4) 10.0 points
b) Find tan .
1. None of these
5
2.
2
25
3.
5
4. 5
008 (part 4 of 4) 10.0 points
d) Find sec .
25
1.
5
2. 2
3. 5
4.
5.
1
2
5
correct
2
6. None of these
Explanation:
5. 2
5
5
5
1
= =
sec =
cos
2
25
5
1
6. correct
2
Explanation:
tan =
1
1
=
cot
2
007 (part 3 of 4) 10.0 points
c) Find csc .
009 (part 1 of 6) 10.0 points
Consider the angle t dened by the point
8 15
,
17 17
to (aqt73) Drill 9 seckin (54330)
y
15
17
17
7.
8
Explanation:
6.
8 15
,
17 17
x
cos t = x =
8
17
17
2.
8
15
correct
3.
8
8
15
17
2.
15
17
3.
8
15
correct
4.
17
1.
1.
4. None of these
15
17
17
6.
15
8
7.
15
Explanation:
5.
5. None of these
8
17
15
7.
8
Explanation:
6.
15
17
010 (part 2 of 6) 10.0 points
b) Find cos t
8
correct
17
17
2.
15
15
3.
8
4. None of these
5.
8
15
15
y
15
tan t = = 17 =
8
x
8
17
8 15
,
17 17
sin t = y =
1.
8
17
011 (part 3 of 6) 10.0 points
c) Find tan t
on the unit circle.
a) Find sin t
(x, y ) =
3
012 (part 4 of 6) 10.0 points
d) Find csc t
8
15
15
2.
8
1.
3. None of these
15
17
17
5.
8
8
6.
17
4.
to (aqt73) Drill 9 seckin (54330)
17
correct
15
Explanation:
7.
csc t =
1
1
17
=
=
15
y
15
17
013 (part 5 of 6) 10.0 points
e) Find sec t.
1.
2.
3.
4.
5.
6.
4
8
x
8
cot t = = 17 =
15
y
15
17
015
10.0 points
Find tan 8 .
1. tan 8 = 1
2. tan 8 is undened
3. tan 8 = 3
17
correct
8
15
8
8
17
17
15
15
17
8
15
4. tan 8 = 0 correct
5. tan 8 = 1
Explanation:
Since 8 = 7 + , the terminal side of the
angle coincides with the negative x-axis, and
tan 8 = tan = 0 .
7. None of these
Explanation:
sec t =
1
1
17
=
=
8
x
8
17
014 (part 6 of 6) 10.0 points
f) Find cot t
1.
2.
3.
4.
5.
6.
17
8
15
8
8
correct
15
8
17
15
17
17
15
7. None of these
Explanation:
016 (part 1 of 4) 10.0 points
a) Without using a calculator, nd two values
of that satisfy the condition
cos =
3
.
2
1. 90 , 270
2. 60 , 300
3. 30 , 330 correct
4. None of these
5. 0 , 180
6. 45 , 315
Explanation:
3
cos =
2
= 30
to (aqt73) Drill 9 seckin (54330)
5
and lies in Quadrant I or IV.
2. 90 , 270
3. None of these
4. 135 , 225 correct
2
1
5. 150 , 210
6. 0 , 180
Explanation:
2
cos =
, so lies in Quadrant II or
2
III.
Thus
1 = 30 and 2 = 360 30 = 330 .
017 (part 2 of 4) 10.0 points
b) Express the above answer in radians.
2
11
1. ,
correct
6
6
7
2. ,
44
1
3. 0 ,
Thus
3
4. ,
22
1 = 180 45 = 135 ,
5. None of these
2 = 180 + 45 = 225 .
5
,
33
Explanation:
6.
30
=
,
180
6
and
330
11
=
.
180
6
019 (part 4 of 4) 10.0 points
d) Express the above answer in radians.
3 5
,
correct
4
4
2 4
2.
,
3
3
1.
3. 0 ,
018 (part 3 of 4) 10.0 points
c) Without using a calculator, nd two values
of that satisfy the condition
2
cos =
2
1. 120 , 240
4.
3
,
22
5. None of these
5 7
,
6
6
Explanation:
6.
to (aqt73) Drill 9 seckin (54330)
135
3
,
=
180
4
6
021 (part 1 of 5) 10.0 points
Suppose
and
csc x = 3,
225
5
=
.
180
4
020
10.0 points
If satises the inequalities
cos > 0 ,
sin cos > 0 ,
in which quadrant must lie?
1. Quadrant IV
2. Quadrant III
3. no such exist
4. Quadrant IV
Explanation:
The inequalities
cos > 0 ,
sin cos > 0
will be satised exactly when
cos > 0 ,
sin > 0 .
But
cos > 0
in Quadrant I, IV ,
Quadrant in I, II .
while
sin > 0
a) Find sin x.
1. None of these
2. 2 2
1
correct
3
2
4.
4
22
5.
3
32
6.
4
Explanation:
x is in Quadrant I.
3.
sin x =
5. Quadrant I correct
Consequently, satises the inequalities only
when lies in
cos x > 0
1
1
=
csc x
3
022 (part 2 of 5) 10.0 points
b) Find cos x.
1. None of these
2. 2 2
32
3.
4
2
4.
4
1
5.
3
22
correct
6.
3
Explanation:
Quadrant I .
cos x =
keywords: trig functions, sin, cos, PlaceUT,
sign, quadrant, Level II,
=
1 sin2 x
1
1
3
2
22
=
3
to (aqt73) Drill 9 seckin (54330)
023 (part 3 of 5) 10.0 points
c) Find tan x.
1.
1
3
2
correct
4
3. 2 2
2.
4. None of these
22
5.
3
32
6.
4
Explanation:
sin x
2
2
1
3
tan x =
= =
cos x
322
4
2
024 (part 4 of 5) 10.0 points
d) Find sec x.
1. 2 2
32
2.
correct
4
22
3.
3
4. None of these
2
5.
4
1
6.
3
Explanation:
2
3
1
32
= =
sec x =
cos x
4
22
2
025 (part 5 of 5) 10.0 points
e) Find cot x.
2
1.
4
7
1
3
32
3.
4
2.
4. None of these
22
5.
3
6. 2 2 correct
Explanation:
4
1
2
= =2 2
cot x =
tan x
2
2
026 (part 1 of 5) 10.0 points
Suppose
sec = 6,
tan < 0
a) Find cos .
1. 35
6 35
2.
35
35
3.
35
35
4.
6
5. None of these
1
6. correct
6
Explanation:
is in Quadrant II since secant and tangent
are both negative.
cos =
1
1
=
sec
6
027 (part 2 of 5) 10.0 points
b) Find sin .
1. None of these
to (aqt73) Drill 9 seckin (54330)
6 35
2.
35
35
3.
correct
6
4. 35
35
5.
35
1
6.
6
Explanation:
sin =
=
3. None of these
6 35
4.
correct
35
5. 35
1
6
Explanation:
6.
35
1
6
6 35
csc =
= =
sin
35
35
35
1 cos2
1
1
6
2
=
35
6
028 (part 3 of 5) 10.0 points
c) Find tan .
35
1.
6
2. None of these
1
3.
6
6 35
4.
35
35
5.
35
6. 35 correct
sin
=
cos
1
1.
6
2. 35
35
3.
correct
35
6 35
4.
35
35
5.
6
6. None of these
Explanation:
1
1
35
35
= =
cot =
tan
35
35
35
Explanation:
tan =
030 (part 5 of 5) 10.0 points
e) Find cot .
35
6 = 35
6
029 (part 4 of 5) 10.0 points
d) Find csc .
35
1.
35
35
2.
6
031 (part 1 of 3) 10.0 points
a) sec x cos x =
1. tan x
2. cot x
3. 1 correct
4. sin x
5. cos x
8
to (aqt73) Drill 9 seckin (54330)
6. 1
Explanation:
sec x cos x =
1
cos x = 1
cos x
032 (part 2 of 3) 10.0 points
b) cot x sin x =
1. cot x
a) Find sin x.
23
1.
3
2. 3
3. 3 3
1
4. correct
2
5. 2
2. cos x correct
6. None of these
3. 1
Explanation:
x is in Quandrant III.
4. tan x
5. 1
sin x = 1 cos2 x
6. sin x
=
Explanation:
cot x sin x =
cos x
sin x = cos x
sin x
033 (part 3 of 3) 10.0 points
c) tan x sec2 x =
2
1
3
2
2
=
1
2
035 (part 2 of 4) 10.0 points
b) Find csc x.
1. 2 correct
1
2.
2
3. 3
1. cot x
2. sin x
3. 1 correct
4. None of these
23
5.
3
6. 3 3
4. tan x
5. 1
6. cos x
Explanation:
Explanation:
2
9
2
2
2
tan x sec x = tan x (tan x + 1) = 1
034 (part 1 of 4) 10.0 points
Suppose
3
3
tan x =
, cos x =
3
2
csc x =
1
= 2
sin x
036 (part 3 of 4) 10.0 points
c) Find sec x.
1. 3
to (aqt73) Drill 9 seckin (54330)
2. 3 3
5. cot2 x
3. None of these
23
correct
4.
3
1
5.
2
10
6. 1
7. 1
8. 0
9. None of these
6. 2
10. cos2 x correct
Explanation:
3
2
23
1
= =
sec x =
cos x
3
3
3
037 (part 4 of 4) 10.0 points
d) Find cot x.
Explanation:
1
tan2 x +
1
039
=
1
= cos2 x
2x
sec
10.0 points
Simpify
(cos t)(1 + tan2 t)
1. None of these
2. 3 correct
1. sec t correct
2. 0
3. 2
4. 3 3
3. 1
4. cot t
1
2
23
6.
3
Explanation:
5.
5. cos t
6. csc t
3
1
3
cot x =
= = 3
tan x
3
3
038
Simpify
10.0 points
1
tan2 x +
1
7. sin t
8. 1
9. tan t
10. None of these
Explanation:
2
1. sin x
2. tan2 x
3. csc2 x
4. sec2 x
(cos t)(1 + tan2 t) = (cos t)(sec2 t)
1
= (cos t)
cos2 t
1
= sec t
=
cos t
to (aqt73) Drill 9 seckin (54330)
040
10.0 points
Simpify
(cot x + csc x)(cot x csc x)
11
6. sin =
1
9
Explanation:
When
tan = 2 2 < 0 ,
1. tan2 x
cos > 0 ,
then lies in Quadrant IV as shown in
2. sec2 x
3. cos2 x
y
4. 0
P = (x, y )
x + y 2 = r2
2
5. sin2 x
x
2
6. csc x
7. cot2 x
P
8. None of these
9. 1
where
10. 1 correct
Explanation:
(cot x + csc x)(cot x csc x)
= cot2 x csc2 x
= 1
041
10.0 points
Find the exact value of sin when
cos > 0 .
tan = 2 2 ,
22
1. sin =
correct
3
2. sin =
1
3
22
3. sin =
9
4. sin =
1
9
22
5. sin =
3
P = (1, 2 2) ,
tan =
y
,
x
sin =
y
.
r
Consequently, r = 3 and
22
sin =
.
3
keywords: PlaceUT, exact value, trig functions, sin, cos, tan, quadrant,