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Math Problems
Algebra 2
Find trigonometric ratios using a Pythagorean or reciprocal identity
Find an ordered pair that satisfies the equation
4
x
+
y
=
6
4 x+y=6
4
x
+
y
=
6
by letting
y
=
−
2
y=-2
y
=
−
2
\newline
The ordered pair is
□
\square
□
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Find an ordered pair that satisfies the equation
x
+
y
=
3
x+y=3
x
+
y
=
3
by letting
x
=
1
x=1
x
=
1
.
\newline
The ordered pair is
□
\square
□
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Find the argument of the complex number
−
3
3
−
9
i
-3 \sqrt{3}-9 i
−
3
3
−
9
i
in the interval
0
≤
θ
<
2
π
0 \leq \theta<2 \pi
0
≤
θ
<
2
π
. Express your answer in terms of
π
\pi
π
.
\newline
Answer:
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Find the argument of the complex number
3
2
+
3
2
i
3 \sqrt{2}+3 \sqrt{2} i
3
2
+
3
2
i
in the interval
0
≤
θ
<
2
π
0 \leq \theta<2 \pi
0
≤
θ
<
2
π
. Express your answer in terms of
π
\pi
π
.
\newline
Answer:
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Find the argument of the complex number
−
3
3
+
0
i
-3 \sqrt{3}+0 i
−
3
3
+
0
i
in the interval
0
≤
θ
<
2
π
0 \leq \theta<2 \pi
0
≤
θ
<
2
π
. Express your answer in terms of
π
\pi
π
.
\newline
Answer:
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Find the argument of the complex number
2
−
2
i
\sqrt{2}-\sqrt{2} i
2
−
2
i
in the interval
0
≤
θ
<
2
π
0 \leq \theta<2 \pi
0
≤
θ
<
2
π
. Express your answer in terms of
π
\pi
π
.
\newline
Answer:
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The area of a triangle is
381
381
381
. Two of the side lengths are
10
10
10
and
93
93
93
and the included angle is acute. 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
2632
2632
2632
. Two of the side lengths are
85
85
85
and
63
63
63
and the included angle is obtuse. Find the measure of the included angle, to the nearest tenth of
a
a
a
degree.
\newline
Answer:
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Question
\newline
Given
tan
A
=
−
11
60
\tan A=-\frac{11}{60}
tan
A
=
−
60
11
and that angle
A
A
A
is in Quadrant IV, find the exact value of
csc
A
\csc A
csc
A
in simplest radical form using a rational denominator.
\newline
Answer Attempt
1
1
1
out of
2
2
2
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Find an angle
θ
\theta
θ
coterminal to
61
2
∘
612^{\circ}
61
2
∘
, 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
−
42
4
∘
-424^{\circ}
−
42
4
∘
, where
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
.
\newline
Answer:
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Given
g
(
x
)
=
5
x
+
5
g(x)=5 x+5
g
(
x
)
=
5
x
+
5
, solve for
x
x
x
when
g
(
x
)
=
0
g(x)=0
g
(
x
)
=
0
.
\newline
Answer:
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Given
f
(
x
)
=
2
x
−
5
f(x)=2 x-5
f
(
x
)
=
2
x
−
5
, solve for
x
x
x
when
f
(
x
)
=
7
f(x)=7
f
(
x
)
=
7
.
\newline
Answer:
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Given
h
(
x
)
=
2
x
−
3
h(x)=2 x-3
h
(
x
)
=
2
x
−
3
, find
h
(
1
)
h(1)
h
(
1
)
.
\newline
Answer:
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Put the following equation of a line into slope-intercept form, simplifying all fractions.
\newline
3
x
+
3
y
=
21
3 x+3 y=21
3
x
+
3
y
=
21
\newline
Answer:
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Solve the following equation for
g
g
g
. Be sure to take into account whether a letter is capitalized or not.
\newline
H
=
3
M
g
−
7
g
H=3 M g-7 g
H
=
3
M
g
−
7
g
\newline
Answer:
g
=
g=
g
=
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Solve the following equation for
b
b
b
. Be sure to take into account whether a letter is capitalized or not.
\newline
b
(
d
+
F
)
=
4
G
b(d+F)=4 G
b
(
d
+
F
)
=
4
G
\newline
Answer:
b
=
b=
b
=
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Solve the following equation for
D
D
D
. Be sure to take into account whether a letter is capitalized or not.
\newline
H
D
=
m
H D=m
HD
=
m
\newline
Answer:
D
=
D=
D
=
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The differentiable functions
x
x
x
and
y
y
y
are related by the following equation:
\newline
sin
(
y
)
=
−
5
x
\sin (y)=-5 x
sin
(
y
)
=
−
5
x
\newline
Also,
d
y
d
t
=
10
\frac{d y}{d t}=10
d
t
d
y
=
10
.
\newline
Find
d
x
d
t
\frac{d x}{d t}
d
t
d
x
when
y
=
−
π
y=-\pi
y
=
−
π
.
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The angle
θ
1
\theta_{1}
θ
1
is located in Quadrant IV, and
cos
(
θ
1
)
=
3
5
\cos \left(\theta_{1}\right)=\frac{3}{5}
cos
(
θ
1
)
=
5
3
.
\newline
What is the value of
sin
(
θ
1
)
\sin \left(\theta_{1}\right)
sin
(
θ
1
)
? Express your answer exactly.
\newline
sin
(
θ
1
)
=
\sin \left(\theta_{1}\right)=
sin
(
θ
1
)
=
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The angle
θ
1
\theta_{1}
θ
1
is located in Quadrant III, and
cos
(
θ
1
)
=
−
13
15
\cos \left(\theta_{1}\right)=-\frac{13}{15}
cos
(
θ
1
)
=
−
15
13
.
\newline
What is the value of
sin
(
θ
1
)
\sin \left(\theta_{1}\right)
sin
(
θ
1
)
? Express your answer exactly.
\newline
sin
(
θ
1
)
=
\sin \left(\theta_{1}\right)=
sin
(
θ
1
)
=
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The angle
θ
1
\theta_{1}
θ
1
is located in Quadrant III, and
cos
(
θ
1
)
=
−
5
8
\cos \left(\theta_{1}\right)=-\frac{5}{8}
cos
(
θ
1
)
=
−
8
5
.
\newline
What is the value of
sin
(
θ
1
)
\sin \left(\theta_{1}\right)
sin
(
θ
1
)
? Express your answer exactly.
\newline
sin
(
θ
1
)
=
\sin \left(\theta_{1}\right)=
sin
(
θ
1
)
=
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The angle
θ
1
\theta_{1}
θ
1
is located in Quadrant II, and
cos
(
θ
1
)
=
−
22
29
\cos \left(\theta_{1}\right)=-\frac{22}{29}
cos
(
θ
1
)
=
−
29
22
.
\newline
What is the value of
sin
(
θ
1
)
\sin \left(\theta_{1}\right)
sin
(
θ
1
)
? Express your answer exactly.
\newline
sin
(
θ
1
)
=
\sin \left(\theta_{1}\right)=
sin
(
θ
1
)
=
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The angle
θ
1
\theta_{1}
θ
1
is located in Quadrant II, and
cos
(
θ
1
)
=
−
12
19
\cos \left(\theta_{1}\right)=-\frac{12}{19}
cos
(
θ
1
)
=
−
19
12
.
\newline
What is the value of
sin
(
θ
1
)
\sin \left(\theta_{1}\right)
sin
(
θ
1
)
? Express your answer exactly.
\newline
sin
(
θ
1
)
=
\sin \left(\theta_{1}\right)=
sin
(
θ
1
)
=
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The graph of a sinusoidal function intersects its midline at
(
0
,
5
)
(0,5)
(
0
,
5
)
and then has a maximum point at
(
0.75
,
7
)
(0.75,7)
(
0.75
,
7
)
.
\newline
Write the formula of the function, where
x
x
x
is entered in radians.
\newline
f
(
x
)
=
□
f(x)=\square
f
(
x
)
=
□
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If
y
=
38
(
1.04
)
x
y=38(1.04)^{x}
y
=
38
(
1.04
)
x
is graphed in the
x
y
x y
x
y
-plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
x
x
-intercept
\newline
(B)
y
y
y
-intercept
\newline
(C) Slope
\newline
(D) The value
y
y
y
approaches as
x
x
x
becomes very large
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If
y
=
15
(
1.08
)
12
x
y=15(1.08)^{12 x}
y
=
15
(
1.08
)
12
x
is graphed in the
x
y
x y
x
y
-plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
x
x
-intercept
\newline
(B)
y
y
y
-intercept
\newline
(C) Slope
\newline
(D) The value
y
y
y
approaches as
x
x
x
increases
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If
y
=
(
x
+
2
)
(
x
+
8
)
y=(x+2)(x+8)
y
=
(
x
+
2
)
(
x
+
8
)
is graphed in the
x
y
x y
x
y
-plane, which of the following characteristics of the graph is displayed as a constant in the equation?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
x
x
-intercept(s)
\newline
(B)
y
y
y
-intercept
\newline
(C)
x
x
x
-coordinate of the vertex
\newline
(D) Minimum
y
y
y
-value
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If
cos
(
θ
)
=
8
17
\cos(\theta)=\frac{8}{17}
cos
(
θ
)
=
17
8
and
0
∘
<
θ
<
9
0
∘
0^\circ<\theta<90^\circ
0
∘
<
θ
<
9
0
∘
, what is
sec
(
θ
)
\sec(\theta)
sec
(
θ
)
? Write your answer in simplified, rationalized form.
sec
(
θ
)
=
\sec(\theta)=
sec
(
θ
)
=
______
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