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Math Problems
Precalculus
Inverses of trigonometric functions
Pluto's distance
(
in billions of kilometers
)
(\text{in billions of kilometers})
(
in billions of kilometers
)
from the sun as a function of time
(
in years
)
(\text{in years})
(
in years
)
can be modeled by a sinusoidal expression of the form
.
.
.
At year
t
=
0
t = 0
t
=
0
, Pluto is at its average distance from the sun, which is
D
D
D
billion kilometers. In
T
T
T
years, it is at its closest point to the sun, which is
d
d
d
billion kilometers away. Find
ω
\omega
ω
.
ω
\omega
ω
should be in radians.
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z=
6
6
6
+
5
5
5
i Find the angle
θ
\theta
θ
(in degrees) that
z
z
z
makes in the complex plane. Round your answer, if necessary, to the nearest tenth. Express
θ
\theta
θ
between
−
π
-\pi
−
π
and
π
\pi
π
.
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z=
4
4
4
−
2
-2
−
2
i Find the angle
θ
\theta
θ
(in degrees) that
z
z
z
makes in the complex plane. Round your answer, if necessary, to the nearest tenth. Express
θ
\theta
θ
between
−
180
-180
−
180
and
180
180
180
.
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In
∠
U
V
W
\angle UVW
∠
U
VW
,
u
=
63
u=63
u
=
63
inches,
v
=
91
v=91
v
=
91
inches and
w
=
60
w=60
w
=
60
inches. Find the measure of
∠
W
\angle W
∠
W
to the nearest degree.
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Find the area in the left tail more extreme than
z
=
−
2.56
z=-2.56
z
=
−
2.56
in a standard normal distribution. Round your answer to four decimal places.
\newline
Area -
□
\square
□
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Find the area in the left tail more extreme than
z
=
−
2.56
z=-2.56
z
=
−
2.56
in a standard normal distribution.
\newline
Round your answer to four decimal places.
\newline
Area -
□
\square
□
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Hiro is riding a carousel that is next to a wall.
\newline
His horizontal distance
C
(
t
)
C(t)
C
(
t
)
(in
m
\mathrm{m}
m
) away from the wall as a function of time
t
t
t
(in seconds) can be modeled by a sinusoidal expression of the form
a
⋅
cos
(
b
⋅
t
)
+
d
a \cdot \cos (b \cdot t)+d
a
⋅
cos
(
b
⋅
t
)
+
d
.
\newline
At
t
=
0
t=0
t
=
0
, when he starts, he is closest to the wall, a distance of
2
m
2 \mathrm{~m}
2
m
away. After
7
π
7 \pi
7
π
seconds he reaches his mid-way point from the wall, which is
7
m
7 \mathrm{~m}
7
m
away.
\newline
Find
C
(
t
)
C(t)
C
(
t
)
.
\newline
t
t
t
should be in radians.
\newline
C
(
t
)
=
C(t)=
C
(
t
)
=
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Convert the angle
θ
=
17
π
18
\theta=\frac{17\pi}{18}
θ
=
18
17
π
radians to degrees.
\newline
Express your answer exactly.
\newline
θ
=
□
∘
\theta=\square^{\circ}
θ
=
□
∘
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Convert the angle
θ
=
8
π
9
\theta=\frac{8 \pi}{9}
θ
=
9
8
π
radians to degrees.
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The questions below are posed in order to help you think about how to find the number of degrees in
7
π
9
\frac{7 \pi}{9}
9
7
π
radians.
\newline
What fraction of a semicircle is an angle that measures
7
π
9
\frac{7 \pi}{9}
9
7
π
radians? Express your answer as a fraction in simplest terms.
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The questions below are posed in order to help you think about how to find the number of degrees in
5
π
12
\frac{5 \pi}{12}
12
5
π
radians.
\newline
What fraction of a semicircle is an angle that measures
5
π
12
\frac{5 \pi}{12}
12
5
π
radians? Express your answer as a fraction in simplest terms.
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The questions below are posed in order to help you think about how to find the number of degrees in
5
π
6
\frac{5 \pi}{6}
6
5
π
radians.
\newline
What fraction of a semicircle is an angle that measures
5
π
6
\frac{5 \pi}{6}
6
5
π
radians? Express your answer as a fraction in simplest terms.
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The area of a parallelogram is
10
10
10
, and the lengths of its sides are
6
6
6
.
9
9
9
and
6
6
6
.
7
7
7
. Determine, to the nearest tenth of a degree, the measure of the acute angle of the parallelogram.
\newline
Answer:
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The area of a parallelogram is
456
456
456
, and the lengths of its sides are
25
25
25
and
62
62
62
. Determine, to the nearest tenth of a degree, the measure of the acute angle of the parallelogram.
\newline
Answer:
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The area of a triangle is
5
5
5
. Two of the side lengths are
1
1
1
.
4
4
4
and
9
9
9
.
6
6
6
and the included angle is obtuse. Find the measure of the included angle, to the nearest tenth of a degree.
\newline
Answer:
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The area of a triangle is
6
6
6
. Two of the side lengths are
9
9
9
.
6
6
6
and
1
1
1
.
5
5
5
and the included angle is obtuse. Find the measure of the included angle, to the nearest tenth of a degree.
\newline
Answer:
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The area of a triangle is
10
10
10
. Two of the side lengths are
5
5
5
.
3
3
3
and
5
5
5
and the included angle is obtuse. Find the measure of the included angle, to the nearest tenth of a degree.
\newline
Answer:
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Convert the angle
θ
=
26
0
∘
\theta=260^{\circ}
θ
=
26
0
∘
to radians.
\newline
Express your answer exactly.
\newline
θ
=
□
radians
\theta=\square \text { radians }
θ
=
□
radians
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Find the direction angle of
u
=
(
−
7
,
−
10
)
\mathbf{u}=(-7,-10)
u
=
(
−
7
,
−
10
)
. Enter your answer as an angle in degrees between
0
∘
0^\circ
0
∘
and
36
0
∘
360^\circ
36
0
∘
rounded to the nearest hundredth.
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Find the direction angle of
u
=
(
−
10
,
7
)
\mathbf{u} = (-10,7)
u
=
(
−
10
,
7
)
. Enter your answer as an angle in degrees between
0
∘
0^\circ
0
∘
and
36
0
∘
360^\circ
36
0
∘
rounded to the nearest hundredth.
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Convert the angle
θ
=
34
5
∘
\theta = 345^\circ
θ
=
34
5
∘
to radians. Express your answer exactly.
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Convert the angle
−
4.5
-4.5
−
4.5
radians to degrees, rounding to the nearest
1
0
t
h
10^{th}
1
0
t
h
.
\newline
Answer:
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Convert the angle
−
2
-2
−
2
.
5
5
5
radians to degrees, rounding to the nearest
10
10
10
th.
\newline
Answer:
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Convert the following angle from degrees to radians. Express your answer in simplest form.
\newline
57
0
∘
570^{\circ}
57
0
∘
\newline
Answer:
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Rotate the yellow dot to a location of
1
1
1
radian. After you rotate the angle, determine the value of
cos
1
\cos 1
cos
1
, to the nearest hundredth.
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Rotate the yellow dot to a location of
3
3
3
radians. After you rotate the angle, determine the value of
csc
3
\csc 3
csc
3
, to the nearest hundredth.
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Rotate the yellow dot to a location of
3
π
2
\frac{3 \pi}{2}
2
3
π
radians. After you rotate the angle, determine the value of
sin
3
π
2
\sin \frac{3 \pi}{2}
sin
2
3
π
, to the nearest hundredth.
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Rotate the yellow dot to a location of
π
2
\frac{\pi}{2}
2
π
radians. After you rotate the angle, determine the value of
tan
π
2
\tan \frac{\pi}{2}
tan
2
π
, to the nearest hundredth.
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Rotate the yellow dot to a location of
2
π
2 \pi
2
π
radians. After you rotate the angle, determine the value of
tan
2
π
\tan 2 \pi
tan
2
π
, to the nearest hundredth.
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Rotate the yellow dot to a location of
3
π
2
\frac{3 \pi}{2}
2
3
π
radians. After you rotate the angle, determine the value of
cos
3
π
2
\cos \frac{3 \pi}{2}
cos
2
3
π
, to the nearest hundredth.
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Rotate the yellow dot to a location of
π
2
\frac{\pi}{2}
2
π
radians. After you rotate the angle, determine the value of
sin
π
2
\sin \frac{\pi}{2}
sin
2
π
, to the nearest hundredth.
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Convert the angle
4
4
4
.
5
5
5
radians to degrees, rounding to the nearest
10
10
10
th.
\newline
Answer:
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Convert the angle
−
4
-4
−
4
.
5
5
5
radians to degrees, rounding to the nearest
10
10
10
th.
\newline
Answer:
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Convert the angle
−
5
-5
−
5
radians to degrees, rounding to the nearest
10
10
10
th.
\newline
Answer:
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Convert the angle
2
2
2
radians to degrees, rounding to the nearest
10
10
10
th.
\newline
Answer:
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Convert the angle
−
1
-1
−
1
radian to degrees, rounding to the nearest
10
10
10
th.
\newline
Answer:
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Convert the angle
−
3
-3
−
3
radians to degrees, rounding to the nearest
10
10
10
th.
\newline
Answer:
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Convert the angle
−
0
-0
−
0
.
5
5
5
radians to degrees, rounding to the nearest
10
10
10
th.
\newline
Answer:
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Convert the angle
3
π
4
\frac{3 \pi}{4}
4
3
π
radians to degrees.
\newline
Answer:
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Convert the angle
−
2
-2
−
2
radians to degrees, rounding to the nearest
10
10
10
th.
\newline
Answer:
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Convert the angle
−
3
-3
−
3
.
5
5
5
radians to degrees, rounding to the nearest
10
10
10
th.
\newline
Answer:
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Convert the angle
−
1
-1
−
1
.
5
5
5
radians to degrees, rounding to the nearest
10
10
10
th.
\newline
Answer:
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Convert the angle
0
0
0
.
5
5
5
radians to degrees, rounding to the nearest
10
10
10
th.
\newline
Answer:
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Convert the angle
7
π
12
\frac{7 \pi}{12}
12
7
π
radians to degrees.
\newline
Answer:
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Convert the angle
5
π
3
\frac{5 \pi}{3}
3
5
π
radians to degrees.
\newline
Answer:
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Convert the angle
5
π
6
\frac{5 \pi}{6}
6
5
π
radians to degrees.
\newline
Answer:
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Convert the angle
7
π
4
\frac{7 \pi}{4}
4
7
π
radians to degrees.
\newline
Answer:
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Convert the angle
5
π
4
\frac{5 \pi}{4}
4
5
π
radians to degrees.
\newline
Answer:
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Convert the angle
9
π
4
\frac{9 \pi}{4}
4
9
π
radians to degrees.
\newline
Answer:
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The median for the given set of six ordered data values is
26
26
26
.
5
5
5
.
\newline
91221
_
4149
91221 \_4149
91221_4149
\newline
What is the missing value?
\newline
The missing value is
□
\square
□
.
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