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Precalculus
Coterminal and reference angles
The graph of a sinusoidal function has a maximum point at
(
0
,
8
)
(0,8)
(
0
,
8
)
and then has a minimum point at
(
5
,
2
)
(5,2)
(
5
,
2
)
.
\newline
Write the formula of the function, where
x
x
x
is entered in radians.
\newline
f(x)=_____
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Without using a calculator, decide whether the function value is positive or negative. (Hint: Consider the radian measures of the quadrantal angles.)
\newline
cos
2
\cos 2
cos
2
\newline
Is the value of the function
cos
2
\cos 2
cos
2
positive or negative?
\newline
positive
\newline
negative
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Find the distance between the points
(
4
,
10
)
(4,10)
(
4
,
10
)
and
(
10
,
10
)
(10,10)
(
10
,
10
)
.
\newline
_
_
_
_
\_\_\_\_
____
units
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Find the distance between the points
(
2
,
10
)
(2,10)
(
2
,
10
)
and
(
9
,
10
)
(9,10)
(
9
,
10
)
.
\newline
____ units
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Find the measure of a negative angle coterminal with
9
0
∘
90^\circ
9
0
∘
.
\newline
_
_
_
_
∘
\_\_\_\_\,^\circ
____
∘
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Find the measure of a negative angle coterminal with
2
0
∘
20^\circ
2
0
∘
.
\newline
____
∘
^\circ
∘
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Find the measure of a negative angle coterminal with
28
0
∘
280^\circ
28
0
∘
.
\newline
_
_
_
_
∘
\_\_\_\_\,^\circ
____
∘
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Find the measure of a negative angle coterminal with
11
0
∘
110^\circ
11
0
∘
.
\newline
____
∘
^\circ
∘
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Find the measure of a negative angle coterminal with
24
0
∘
240^\circ
24
0
∘
.
\newline
____
∘
^\circ
∘
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Find the measure of a negative angle coterminal with
34
0
∘
340^\circ
34
0
∘
.
\newline
____
∘
^\circ
∘
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Find the measure of a negative angle coterminal with
17
0
∘
170^\circ
17
0
∘
.
\newline
____
∘
^\circ
∘
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Find the measure of a negative angle coterminal with
4
0
∘
40^\circ
4
0
∘
.
\newline
____
∘
^\circ
∘
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Find the measure of a negative angle coterminal with
6
0
∘
60^\circ
6
0
∘
.
\newline
____
∘
^\circ
∘
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Find the measure of a negative angle coterminal with
12
0
∘
120^\circ
12
0
∘
.
\newline
____
∘
^\circ
∘
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Find the measure of a negative angle coterminal with
29
0
∘
290^\circ
29
0
∘
.
\newline
____
∘
^\circ
∘
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Find the measure of a negative angle coterminal with
13
0
∘
130^\circ
13
0
∘
.
\newline
____
∘
^\circ
∘
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Find the measure of a negative angle coterminal with
5
0
∘
50^\circ
5
0
∘
.
\newline
____
∘
^\circ
∘
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Find the measure of a negative angle coterminal with
23
0
∘
230^\circ
23
0
∘
.
\newline
____
∘
^\circ
∘
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Find the measure of a negative angle coterminal with
14
0
∘
140^\circ
14
0
∘
.
\newline
____
∘
^\circ
∘
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Find the measure of a negative angle coterminal with
1
0
∘
10^\circ
1
0
∘
.
\newline
____
∘
^\circ
∘
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Find the measure of a negative angle coterminal with
19
0
∘
190^\circ
19
0
∘
.
\newline
____
∘
^\circ
∘
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Find the measure of a negative angle coterminal with
10
0
∘
100^\circ
10
0
∘
.
\newline
____
∘
^\circ
∘
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Find the measure of a negative angle coterminal with
20
0
∘
200^\circ
20
0
∘
.
\newline
____
∘
^\circ
∘
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Find the measure of a negative angle coterminal with
27
0
∘
270^\circ
27
0
∘
.
\newline
____
∘
^\circ
∘
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Find the measure of a negative angle coterminal with
16
0
∘
160^\circ
16
0
∘
.
\newline
____
∘
^\circ
∘
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The graph of a sinusoidal function has a minimum point at
(
0
,
10
)
(0,10)
(
0
,
10
)
and then has a maximum point at
(
2
,
−
4
)
(2,-4)
(
2
,
−
4
)
. Write the formula of the function, where
X
X
X
is entered in radians.
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The graph of a sinusoidal function intersects its midline at
(
0
,
−
6
)
(0,-6)
(
0
,
−
6
)
and then has a minimum point at
(
2.5
,
−
9
)
(2.5,-9)
(
2.5
,
−
9
)
.
\newline
Write the formula of the function, where
x
x
x
is entered in radians.
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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
.)
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Find an angle
θ
\theta
θ
coterminal to
−
28
3
∘
-283^{\circ}
−
28
3
∘
, where
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
.
\newline
Answer:
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Find an angle
θ
\theta
θ
coterminal to
−
25
3
∘
-253^{\circ}
−
25
3
∘
, where
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
.
\newline
Answer:
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A solid is cut by a plane that is perpendicular to its base, forming a two-dimensional cross section in the shape of a rectangle. Which of the following solids could have resulted in that cross section?
\newline
rectangular pyramid
\newline
sphere
\newline
rectangular prism
\newline
right cone
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