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Math Problems
Algebra 2
Convert between radians and degrees
Which of the following radian measures is equal to
1
,
08
0
∘
1,080^\circ
1
,
08
0
∘
?
\newline
(The number of degrees of arc in a circle is
36
0
∘
360^\circ
36
0
∘
. The number of radians of arc in a circle is
2
π
2\pi
2
π
.)
\newline
Choose
1
1
1
answer:
\newline
(A)
3
π
3\pi
3
π
radians
\newline
(B)
6
π
6\pi
6
π
radians
\newline
(C)
10
π
10\pi
10
π
radians
\newline
(D)
12
π
12\pi
12
π
radians
Get tutor help
How many radians is
4
5
∘
45^\circ
4
5
∘
?
\newline
Choices:
\newline
(A)
π
/
2
\pi /2
π
/2
radians
\newline
(B)
π
/
3
\pi /3
π
/3
radians
\newline
(C)
π
/
6
\pi /6
π
/6
radians
\newline
(D)
π
/
4
\pi /4
π
/4
radians
Get tutor help
How many radians is
9
0
∘
90^\circ
9
0
∘
?
\newline
Choices:
\newline
(A)
π
/
6
\pi /6
π
/6
radians
\newline
(B)
π
/
3
\pi /3
π
/3
radians
\newline
(C)
π
/
2
\pi /2
π
/2
radians
\newline
(D)
π
/
4
\pi /4
π
/4
radians
Get tutor help
How many radians is
3
0
∘
30^\circ
3
0
∘
?
\newline
Choices:
\newline
(A)
π
/
6
\pi /6
π
/6
radians
\newline
(B)
π
/
3
\pi /3
π
/3
radians
\newline
(C)
π
/
2
\pi /2
π
/2
radians
\newline
(D)
π
/
4
\pi /4
π
/4
radians
Get tutor help
How many radians is
6
0
∘
60^\circ
6
0
∘
?
\newline
Choices:
\newline
(A)
π
/
4
\pi /4
π
/4
radians
\newline
(B)
π
/
2
\pi /2
π
/2
radians
\newline
(C)
π
/
6
\pi /6
π
/6
radians
\newline
(D)
π
/
3
\pi /3
π
/3
radians
Get tutor help
What is the amplitude of
y
=
−
4
cos
(
5
x
−
9
)
−
7
y=-4 \cos (5 x-9)-7
y
=
−
4
cos
(
5
x
−
9
)
−
7
?
\newline
□
\square
□
units
Get tutor help
Which of the following radian measures is equal to
72
0
∘
720^\circ
72
0
∘
? (The number of degrees of arc in a circle is
36
0
∘
360^\circ
36
0
∘
. The number of radians of arc in a circle is
2
π
2\pi
2
π
.)
Get tutor help
Consider the function
f
(
θ
)
=
3
sin
(
2
θ
)
f(\theta)=3 \sin (2 \theta)
f
(
θ
)
=
3
sin
(
2
θ
)
where
θ
\theta
θ
represents a number of radians.
\newline
a. Complete the following table of values.
\newline
\begin{tabular}{|c|c|}
\newline
\hline
θ
\theta
θ
&
f
(
θ
)
f(\theta)
f
(
θ
)
\\
\newline
\hline
0
0
0
&
0
0
0
\\
\newline
\hline
π
4
\frac{\pi}{4}
4
π
& \\
\newline
\hline
π
2
\frac{\pi}{2}
2
π
& \\
\newline
\hline
3
π
4
\frac{3 \pi}{4}
4
3
π
& \\
\newline
\hline
π
\pi
π
& \\
\newline
\hline
\newline
\end{tabular}
\newline
b. Graph the function
f
f
f
below.
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Which of the following radian measures is equal to
\newline
16
5
∘
165^\circ
16
5
∘
?
\newline
Choose
1
1
1
answer:
\newline
(A)
\newline
5
π
12
\frac{5\pi}{12}
12
5
π
radians
\newline
(B)
\newline
7
π
12
\frac{7\pi}{12}
12
7
π
radians
\newline
(C)
\newline
5
π
6
\frac{5\pi}{6}
6
5
π
radians
\newline
(D)
\newline
11
π
12
\frac{11\pi}{12}
12
11
π
radians
Get tutor help
For which values is
tan
θ
\tan \theta
tan
θ
positive?
\newline
A. all radian values between
0
0
0
and
π
\pi
π
\newline
B. all radian values between
π
4
\frac{\pi}{4}
4
π
and
3
π
4
\frac{3\pi}{4}
4
3
π
\newline
C. all radian values between
π
2
\frac{\pi}{2}
2
π
and
π
\pi
π
\newline
D. all radian values between
π
\pi
π
and
3
π
2
\frac{3\pi}{2}
2
3
π
Get tutor help
Which of the following radian measures is equal to
9
0
∘
90^{\circ}
9
0
∘
?
\newline
Choose
1
1
1
answer:
\newline
(A)
π
3
\frac{\pi}{3}
3
π
radians
\newline
(B)
π
4
\frac{\pi}{4}
4
π
radians
\newline
(C)
π
2
\frac{\pi}{2}
2
π
radians
\newline
(D)
π
6
\frac{\pi}{6}
6
π
radians
Get tutor help
Which of the following radian measures is equal to
54
0
∘
540^\circ
54
0
∘
?
\newline
(The number of degrees of arc in a circle is
36
0
∘
360^\circ
36
0
∘
. The number of radians of arc in a circle is
2
π
2\pi
2
π
.)
\newline
Choose
1
1
1
answer:
\newline
(A)
3
π
3\pi
3
π
radians
\newline
(B)
6
π
6\pi
6
π
radians
\newline
(C)
9
π
9\pi
9
π
radians
\newline
(D)
12
π
12\pi
12
π
radians
Get tutor help
Which of the following radian measures is equal to
2
,
88
0
∘
2,880^{\circ}
2
,
88
0
∘
?
\newline
(The number of degrees of arc in a circle is
36
0
∘
360^{\circ}
36
0
∘
. The number of radians of arc in a circle is
2
π
2\pi
2
π
.)
\newline
Choose
1
1
1
answer:
\newline
(A)
4
π
4\pi
4
π
radians
\newline
(B)
8
π
8\pi
8
π
radians
\newline
(C)
12
π
12\pi
12
π
radians
\newline
(D)
16
π
16\pi
16
π
radians
Get tutor help
Which of the following radian measures is equal to
4
5
∘
45^{\circ}
4
5
∘
?
\newline
Choose
1
1
1
answer:
\newline
(A)
π
2
\frac{\pi}{2}
2
π
radians
\newline
(B)
π
3
\frac{\pi}{3}
3
π
radians
\newline
(C)
π
4
\frac{\pi}{4}
4
π
radians
\newline
(D)
π
6
\frac{\pi}{6}
6
π
radians
Get tutor help
Which of the following radian measures is equal to
1
5
∘
15^{\circ}
1
5
∘
?
\newline
Choose
1
1
1
answer:
\newline
(A)
π
12
\frac{\pi}{12}
12
π
radians
\newline
(B)
π
6
\frac{\pi}{6}
6
π
radians
\newline
(C)
π
3
\frac{\pi}{3}
3
π
radians
\newline
(D)
π
4
\frac{\pi}{4}
4
π
radians
Get tutor help
Which of the following radian measures is equal to
16
5
∘
165^{\circ}
16
5
∘
?
\newline
Choose
1
1
1
answer:
\newline
(A)
5
π
12
\frac{5\pi}{12}
12
5
π
radians
\newline
(B)
7
π
12
\frac{7\pi}{12}
12
7
π
radians
\newline
(C)
5
π
6
\frac{5\pi}{6}
6
5
π
radians
\newline
(D)
11
π
12
\frac{11\pi}{12}
12
11
π
radians
Get tutor help
Which of the following radian measures is equal to
7
5
∘
75^{\circ}
7
5
∘
?
\newline
Choose
1
1
1
answer:
\newline
(A)
π
12
\frac{\pi}{12}
12
π
radians
\newline
(B)
π
3
\frac{\pi}{3}
3
π
radians
\newline
(C)
5
π
12
\frac{5\pi}{12}
12
5
π
radians
\newline
(D)
7
π
12
\frac{7\pi}{12}
12
7
π
radians
Get tutor help
If
θ
=
22
5
∘
\theta=225^{\circ}
θ
=
22
5
∘
, what is the value of
θ
\theta
θ
in radians?
\newline
Choose
1
1
1
answer:
\newline
(A)
4
π
3
\frac{4\pi}{3}
3
4
π
\newline
(B)
5
π
4
\frac{5\pi}{4}
4
5
π
\newline
(C)
2
π
5
\frac{2\pi}{5}
5
2
π
\newline
(D)
7
π
6
\frac{7\pi}{6}
6
7
π
Get tutor help
Which of the following is equivalent to the value of
(
5
π
9
c
+
13
π
18
c
−
17
π
6
c
)
(\frac{5\pi}{9}c + \frac{13\pi}{18}c - \frac{17\pi}{6}c)
(
9
5
π
c
+
18
13
π
c
−
6
17
π
c
)
when converted to degrees?
\newline
(A)
2
0
∘
20^\circ
2
0
∘
\newline
(B)
8
0
∘
80^\circ
8
0
∘
\newline
(C)
28
0
∘
280^\circ
28
0
∘
\newline
(D)
32
0
∘
320^\circ
32
0
∘
Get tutor help
Which of the following is equivalent to the value of
(
5
π
9
+
13
π
18
−
17
π
6
)
(\frac{5\pi}{9}+\frac{13\pi}{18}-\frac{17\pi}{6})
(
9
5
π
+
18
13
π
−
6
17
π
)
when converted to degrees?
\newline
(A)
2
0
∘
20^\circ
2
0
∘
\newline
(B)
8
0
∘
80^\circ
8
0
∘
\newline
(C)
28
0
∘
280^\circ
28
0
∘
\newline
(D)
32
0
∘
320^\circ
32
0
∘
Get tutor help
Which of the following radian measures is equal to
72
0
∘
720^{\circ}
72
0
∘
?
\newline
(The number of degrees of arc in a circle is
360
360
360
. The number of radians of arc in a circle is
2
π
2 \pi
2
π
.)
\newline
Choose
1
1
1
answer:
\newline
(A)
π
\pi
π
radians
\newline
(B)
2
π
2 \pi
2
π
radians
\newline
(C)
4
π
4 \pi
4
π
radians
\newline
(D)
8
π
8 \pi
8
π
radians
Get tutor help
If
x
∘
x^{\circ}
x
∘
is equal to
7
π
7 \pi
7
π
radians, what is the value of
x
x
x
?
\newline
(The number of degrees of arc in a circle is
360
360
360
. The number of radians of arc in a circle is
2
π
2 \pi
2
π
.)
Get tutor help
Which of the following radian measures is equal to
36
0
∘
360^{\circ}
36
0
∘
?
\newline
(The number of degrees of arc in a circle is
360
360
360
. The number of radians of arc in a circle is
2
π
2 \pi
2
π
.)
\newline
Choose
1
1
1
answer:
\newline
(A)
π
2
\frac{\pi}{2}
2
π
radians
\newline
(B)
π
\pi
π
radians
\newline
(C)
2
π
2 \pi
2
π
radians
\newline
D)
3
π
3 \pi
3
π
radians
Get tutor help
Which of the following radian measures is equal to
18
0
∘
180^{\circ}
18
0
∘
?
\newline
(The number of degrees of arc in a circle is
360
360
360
. The number of radians of arc in a circle is
2
π
2 \pi
2
π
.)
\newline
Choose
1
1
1
answer:
\newline
(A)
π
2
\frac{\pi}{2}
2
π
radians
\newline
(B)
π
3
\frac{\pi}{3}
3
π
radians
\newline
C)
π
4
\frac{\pi}{4}
4
π
radians
\newline
(D)
π
\pi
π
radians
Get tutor help
Which of the following degree measures is equal to
3
π
3 \pi
3
π
radians?
\newline
(The number of degrees of arc in a circle is
360
360
360
. The number of radians of arc in a circle is
2
π
2 \pi
2
π
.)
\newline
Choose
1
1
1
answer:
\newline
(A)
6
0
∘
60^{\circ}
6
0
∘
\newline
(B)
12
0
∘
120^{\circ}
12
0
∘
\newline
(C)
18
0
∘
180^{\circ}
18
0
∘
\newline
(D)
54
0
∘
540^{\circ}
54
0
∘
Get tutor help
Which of the following radian measures is equal to
2
,
88
0
∘
2,880^{\circ}
2
,
88
0
∘
?
\newline
(The number of degrees of arc in a circle is
360
360
360
. The number of radians of arc in a circle is
2
π
2 \pi
2
π
.)
\newline
Choose
1
1
1
answer:
\newline
(A)
4
π
4 \pi
4
π
radians
\newline
(B)
8
π
8 \pi
8
π
radians
\newline
(C)
12
π
12 \pi
12
π
radians
\newline
(D)
16
π
16 \pi
16
π
radians
Get tutor help
Which of the following radian measures is equal to
1
,
08
0
∘
1,080^{\circ}
1
,
08
0
∘
?
\newline
(The number of degrees of arc in a circle is
360
360
360
. The number of radians of arc in a circle is
2
π
2 \pi
2
π
.)
\newline
Choose
1
1
1
answer:
\newline
(A)
3
π
3 \pi
3
π
radians
\newline
(B)
6
π
6 \pi
6
π
radians
\newline
(C)
10
π
10 \pi
10
π
radians
\newline
(D)
12
π
12 \pi
12
π
radians
Get tutor help
Which of the following radian measures is equal to
54
0
∘
540^{\circ}
54
0
∘
?
\newline
(The number of degrees of arc in a circle is
360
360
360
. The number of radians of arc in a circle is
2
π
2 \pi
2
π
.)
\newline
Choose
1
1
1
answer:
\newline
(A)
3
π
3 \pi
3
π
radians
\newline
(B)
6
π
6 \pi
6
π
radians
\newline
(C)
9
π
9 \pi
9
π
radians
\newline
(D)
12
π
12 \pi
12
π
radians
Get tutor help
If
a
π
a \pi
aπ
radians is equal to
1
1
1
,
440
440
440
degrees, what is the value of
a
a
a
?
\newline
(The number of degrees of arc in a circle is
360
360
360
. The number of radians of arc in a circle is
2
π
2 \pi
2
π
.)
Get tutor help
If
a
π
a \pi
aπ
radians is equal to
900
900
900
degrees, what is the value of
a
a
a
?
\newline
(The number of degrees of arc in a circle is
360
360
360
. The number of radians of arc in a circle is
2
π
2 \pi
2
π
.)
Get tutor help
Which of the following radian measures is equal to
10
5
∘
105^{\circ}
10
5
∘
?
\newline
Choose
1
1
1
answer:
\newline
(A)
7
π
12
\frac{7 \pi}{12}
12
7
π
radians
\newline
(B)
11
π
12
\frac{11 \pi}{12}
12
11
π
radians
\newline
(C)
13
π
12
\frac{13 \pi}{12}
12
13
π
radians
\newline
(D)
17
π
12
\frac{17 \pi}{12}
12
17
π
radians
Get tutor help
Which of the following radian measures is equal to
30
0
∘
300^{\circ}
30
0
∘
?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
π
3
\frac{2 \pi}{3}
3
2
π
radians
\newline
B
4
π
3
\frac{4 \pi}{3}
3
4
π
radians
\newline
(C)
5
π
3
\frac{5 \pi}{3}
3
5
π
radians
\newline
(D)
7
π
3
\frac{7 \pi}{3}
3
7
π
radians
Get tutor help
Which of the following radian measures is equal to
4
5
∘
45^{\circ}
4
5
∘
?
\newline
Choose
1
1
1
answer:
\newline
(A)
π
2
\frac{\pi}{2}
2
π
radians
\newline
B
π
3
\frac{\pi}{3}
3
π
radians
\newline
(C)
π
4
\frac{\pi}{4}
4
π
radians
\newline
(D)
π
6
\frac{\pi}{6}
6
π
radians
Get tutor help
Which of the following radian measures is equal to
3
0
∘
30^{\circ}
3
0
∘
?
\newline
Choose
1
1
1
answer:
\newline
(A)
π
3
\frac{\pi}{3}
3
π
radians
\newline
(B)
π
6
\frac{\pi}{6}
6
π
radians
\newline
(C)
π
8
\frac{\pi}{8}
8
π
radians
\newline
(D)
π
\pi
π
radians
Get tutor help
Which of the following radian measures is equal to
31
5
∘
315^{\circ}
31
5
∘
?
\newline
Choose
1
1
1
answer:
\newline
(A)
5
π
4
\frac{5 \pi}{4}
4
5
π
radians
\newline
B
7
π
4
\frac{7 \pi}{4}
4
7
π
radians
\newline
(C)
9
π
4
\frac{9 \pi}{4}
4
9
π
radians
\newline
(D)
11
π
4
\frac{11 \pi}{4}
4
11
π
radians
Get tutor help
Which of the following radian measures is equal to
16
5
∘
165^{\circ}
16
5
∘
?
\newline
Choose
1
1
1
answer:
\newline
(A)
5
π
12
\frac{5 \pi}{12}
12
5
π
radians
\newline
(B)
7
π
12
\frac{7 \pi}{12}
12
7
π
radians
\newline
(C)
5
π
6
\frac{5 \pi}{6}
6
5
π
radians
\newline
(D)
11
π
12
\frac{11 \pi}{12}
12
11
π
radians
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Which of the following radian measures is equal to
15
0
∘
150^{\circ}
15
0
∘
?
\newline
Choose
1
1
1
answer:
\newline
(A)
π
3
\frac{\pi}{3}
3
π
radians
\newline
(B)
π
2
\frac{\pi}{2}
2
π
radians
\newline
(C)
2
π
3
\frac{2 \pi}{3}
3
2
π
radians
\newline
(D)
5
π
6
\frac{5 \pi}{6}
6
5
π
radians
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Which of the following radian measures is equal to
12
0
∘
120^{\circ}
12
0
∘
?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
π
3
\frac{2 \pi}{3}
3
2
π
radians
\newline
(B)
π
\pi
π
radians
\newline
(C)
4
π
3
\frac{4 \pi}{3}
3
4
π
radians
\newline
(D)
5
π
3
\frac{5 \pi}{3}
3
5
π
radians
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Which of the following radian measures is equal to
24
0
∘
240^{\circ}
24
0
∘
?
\newline
Choose
1
1
1
answer:
\newline
(A)
4
π
3
\frac{4 \pi}{3}
3
4
π
radians
\newline
B
5
π
3
\frac{5 \pi}{3}
3
5
π
radians
\newline
(C)
7
π
3
\frac{7 \pi}{3}
3
7
π
radians
\newline
(D)
11
π
3
\frac{11 \pi}{3}
3
11
π
radians
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Which of the following radian measures is equal to
7
5
∘
75^{\circ}
7
5
∘
?
\newline
Choose
1
1
1
answer:
\newline
(A)
π
12
\frac{\pi}{12}
12
π
radians
\newline
B
π
3
\frac{\pi}{3}
3
π
radians
\newline
(C)
5
π
12
\frac{5 \pi}{12}
12
5
π
radians
\newline
(D)
7
π
12
\frac{7 \pi}{12}
12
7
π
radians
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Which of the following radian measures is equal to
33
0
∘
330^{\circ}
33
0
∘
?
\newline
Choose
1
1
1
answer:
\newline
(A)
15
π
6
\frac{15 \pi}{6}
6
15
π
radians
\newline
B
7
π
6
\frac{7 \pi}{6}
6
7
π
radians
\newline
(C)
11
π
6
\frac{11 \pi}{6}
6
11
π
radians
\newline
(D)
13
π
6
\frac{13 \pi}{6}
6
13
π
radians
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Which of the following radian measures is equal to
13
5
∘
135^{\circ}
13
5
∘
?
\newline
Choose
1
1
1
answer:
\newline
(A)
π
4
\frac{\pi}{4}
4
π
radians
\newline
(B)
π
2
\frac{\pi}{2}
2
π
radians
\newline
(C)
3
π
4
\frac{3 \pi}{4}
4
3
π
radians
\newline
(D)
π
\pi
π
radians
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Which of the following radian measures is equal to
22
5
∘
225^{\circ}
22
5
∘
?
\newline
Choose
1
1
1
answer:
\newline
(A)
π
4
\frac{\pi}{4}
4
π
radians
\newline
B
π
2
\frac{\pi}{2}
2
π
radians
\newline
(C)
3
π
4
\frac{3 \pi}{4}
4
3
π
radians
\newline
(D)
5
π
4
\frac{5 \pi}{4}
4
5
π
radians
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Which of the following radian measures is equal to
9
0
∘
90^{\circ}
9
0
∘
?
\newline
Choose
1
1
1
answer:
\newline
(A)
π
3
\frac{\pi}{3}
3
π
radians
\newline
B
π
4
\frac{\pi}{4}
4
π
radians
\newline
(C)
π
2
\frac{\pi}{2}
2
π
radians
\newline
(D)
π
6
\frac{\pi}{6}
6
π
radians
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How many radians is
6
0
∘
60^\circ
6
0
∘
?
\newline
Choices:
\newline
[
A
]
π
3
radians
[A]\frac{\pi}{3}\text{ radians}
[
A
]
3
π
radians
\newline
[
B
]
π
2
radians
[B]\frac{\pi}{2}\text{ radians}
[
B
]
2
π
radians
\newline
[
C
]
π
4
radians
[C]\frac{\pi}{4}\text{ radians}
[
C
]
4
π
radians
\newline
[
D
]
π
6
radians
[D]\frac{\pi}{6}\text{ radians}
[
D
]
6
π
radians
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