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Math Problems
Precalculus
Find trigonometric ratios using multiple identities
If
x
+
9
y
=
−
8
\mathbf{x}+\mathbf{9 y}=-\mathbf{8}
x
+
9y
=
−
8
is a true equation, what would be the value of
2
+
x
+
9
y
\mathbf{2}+\mathbf{x}+\mathbf{9 y}
2
+
x
+
9y
?
\newline
Answer:
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If
6
x
+
9
y
=
−
9
6 x+9 y=-9
6
x
+
9
y
=
−
9
is a true equation, what would be the value of
−
3
+
6
x
+
9
y
?
-3+6 x+9 y ?
−
3
+
6
x
+
9
y
?
\newline
Answer:
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If
−
3
x
−
7
y
=
−
1
-\mathbf{3 x}-\mathbf{7 y}=-\mathbf{1}
−
3x
−
7y
=
−
1
is a true equation, what would be the value of
−
3
(
−
3
x
−
7
y
)
-3(-3 x-7 y)
−
3
(
−
3
x
−
7
y
)
?
\newline
Answer:
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If
−
4
x
+
3
y
=
8
-\mathbf{4 x}+\mathbf{3 y}=8
−
4x
+
3y
=
8
is a true equation, what would be the value of
−
3
(
−
4
x
+
3
y
)
-\mathbf{3}(-\mathbf{4 x}+\mathbf{3 y})
−
3
(
−
4x
+
3y
)
?
\newline
Answer:
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If
7
x
−
6
y
=
−
9
7 \mathbf{x}-6 \mathbf{y}=-9
7
x
−
6
y
=
−
9
is a true equation, what would be the value of
−
3
(
7
x
−
6
y
)
-\mathbf{3}(7 \mathrm{x}-6 \mathbf{y})
−
3
(
7
x
−
6
y
)
?
\newline
Answer:
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If
8
x
+
7
y
=
6
8 x+7 y=6
8
x
+
7
y
=
6
is a true equation, what would be the value of
8
x
+
7
y
+
9
?
8 x+7 y+9 ?
8
x
+
7
y
+
9
?
\newline
Answer:
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If
9
x
+
y
=
−
1
\mathbf{9 x}+\mathbf{y}=-\mathbf{1}
9x
+
y
=
−
1
is a true equation, what would be the value of
−
5
+
9
x
+
y
-\mathbf{5}+\mathbf{9 x}+\mathbf{y}
−
5
+
9x
+
y
?
\newline
Answer:
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Find an expression which represents the difference when
(
−
8
x
−
8
y
)
(-8 x-8 y)
(
−
8
x
−
8
y
)
is subtracted from
(
−
x
+
9
y
)
(-x+9 y)
(
−
x
+
9
y
)
in simplest terms.
\newline
Answer:
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Given
f
(
x
)
=
3
csc
(
3
x
)
f(x)=3 \csc (3 x)
f
(
x
)
=
3
csc
(
3
x
)
, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
.
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
E
=
[
3
5
−
1
1
]
and
A
=
[
−
2
2
3
3
5
−
2
]
\begin{array}{l} E=\left[\begin{array}{rr} 3 & 5 \\ -1 & 1 \end{array}\right] \text { and } A=\left[\begin{array}{rrr} -2 & 2 & 3 \\ 3 & 5 & -2 \end{array}\right] \end{array}
E
=
[
3
−
1
5
1
]
and
A
=
[
−
2
3
2
5
3
−
2
]
\newline
Let
H
=
E
A
\mathrm{H}=\mathrm{EA}
H
=
EA
. Find
H
\mathrm{H}
H
.
\newline
H
=
\mathbf{H}=
H
=
Get tutor help
F
=
[
1
2
−
2
3
]
and
E
=
[
0
−
1
5
3
2
1
]
\begin{array}{l} F=\left[\begin{array}{rr} 1 & 2 \\ -2 & 3 \end{array}\right] \text { and } E=\left[\begin{array}{rrr} 0 & -1 & 5 \\ 3 & 2 & 1 \end{array}\right] \end{array}
F
=
[
1
−
2
2
3
]
and
E
=
[
0
3
−
1
2
5
1
]
\newline
Let
H
=
F
E
\mathrm{H}=\mathrm{FE}
H
=
FE
. Find
H
\mathrm{H}
H
.
\newline
H
=
\mathbf{H}=
H
=
Get tutor help
E
=
[
5
3
−
2
1
4
1
]
and
D
=
[
−
2
−
1
5
0
]
\begin{array}{l} \mathrm{E}=\left[\begin{array}{rr} 5 & 3 \\ -2 & 1 \\ 4 & 1 \end{array}\right] \text { and } \mathrm{D}=\left[\begin{array}{rr} -2 & -1 \\ 5 & 0 \end{array}\right] \end{array}
E
=
⎣
⎡
5
−
2
4
3
1
1
⎦
⎤
and
D
=
[
−
2
5
−
1
0
]
\newline
Let
H
=
E
D
\mathrm{H}=\mathrm{ED}
H
=
ED
. Find
H
\mathrm{H}
H
.
\newline
H
=
\mathbf{H}=
H
=
Get tutor help
Let
f
(
x
)
=
x
f(x)=\sqrt{x}
f
(
x
)
=
x
.
\newline
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
Let
f
(
x
)
=
x
−
2
f(x)=x^{-2}
f
(
x
)
=
x
−
2
.
\newline
f
′
(
2
)
=
f^{\prime}(2)=
f
′
(
2
)
=
Get tutor help
Let
h
(
x
)
=
x
2
3
h(x)=\sqrt[3]{x^{2}}
h
(
x
)
=
3
x
2
.
\newline
h
′
(
x
)
=
h^{\prime}(x)=
h
′
(
x
)
=
Get tutor help
The angle
θ
1
\theta_{1}
θ
1
is located in Quadrant
\newline
I, and
sin
(
θ
1
)
=
1
2
\sin \left(\theta_{1}\right)=\frac{1}{2}
sin
(
θ
1
)
=
2
1
.
\newline
What is the value of
cos
(
θ
1
)
\cos \left(\theta_{1}\right)
cos
(
θ
1
)
?
\newline
Express your answer exactly.
\newline
cos
(
θ
1
)
=
\cos \left(\theta_{1}\right)=
cos
(
θ
1
)
=
Get tutor help
The angle
θ
1
\theta_{1}
θ
1
is located in Quadrant II, and
cos
(
θ
1
)
=
−
2
11
\cos \left(\theta_{1}\right)=-\frac{2}{11}
cos
(
θ
1
)
=
−
11
2
.
\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
)
=
Get tutor help
The angle
θ
1
\theta_{1}
θ
1
is located in Quadrant II, and
sin
(
θ
1
)
=
1
4
\sin \left(\theta_{1}\right)=\frac{1}{4}
sin
(
θ
1
)
=
4
1
.
\newline
What is the value of
cos
(
θ
1
)
\cos \left(\theta_{1}\right)
cos
(
θ
1
)
? Express your answer exactly.
\newline
cos
(
θ
1
)
=
\cos \left(\theta_{1}\right)=
cos
(
θ
1
)
=
Get tutor help
The angle
θ
1
\theta_{1}
θ
1
is located in Quadrant
\newline
I, and
sin
(
θ
1
)
=
11
61
\sin \left(\theta_{1}\right)=\frac{11}{61}
sin
(
θ
1
)
=
61
11
.
\newline
What is the value of
cos
(
θ
1
)
\cos \left(\theta_{1}\right)
cos
(
θ
1
)
?
\newline
Express your answer exactly.
\newline
cos
(
θ
1
)
=
\cos \left(\theta_{1}\right)=
cos
(
θ
1
)
=
Get tutor help
The angle
θ
1
\theta_{1}
θ
1
is located in Quadrant
\newline
I, and
cos
(
θ
1
)
=
10
17
\cos \left(\theta_{1}\right)=\frac{10}{17}
cos
(
θ
1
)
=
17
10
.
\newline
What is the value of
sin
(
θ
1
)
\sin \left(\theta_{1}\right)
sin
(
θ
1
)
?
\newline
Express your answer exactly.
\newline
sin
(
θ
1
)
=
\sin \left(\theta_{1}\right)=
sin
(
θ
1
)
=
Get tutor help
The angle
θ
1
\theta_{1}
θ
1
is located in Quadrant
\newline
I, and
cos
(
θ
1
)
=
3
8
\cos \left(\theta_{1}\right)=\frac{3}{8}
cos
(
θ
1
)
=
8
3
.
\newline
What is the value of
sin
(
θ
1
)
\sin \left(\theta_{1}\right)
sin
(
θ
1
)
?
\newline
Express your answer exactly.
\newline
sin
(
θ
1
)
=
\sin \left(\theta_{1}\right)=
sin
(
θ
1
)
=
Get tutor help
The angle
θ
1
\theta_{1}
θ
1
is located in Quadrant IV, and
sin
(
θ
1
)
=
−
24
25
\sin \left(\theta_{1}\right)=-\frac{24}{25}
sin
(
θ
1
)
=
−
25
24
.
\newline
What is the value of
cos
(
θ
1
)
\cos \left(\theta_{1}\right)
cos
(
θ
1
)
? Express your answer exactly.
\newline
cos
(
θ
1
)
=
\cos \left(\theta_{1}\right)=
cos
(
θ
1
)
=
Get tutor help
The angle
θ
1
\theta_{1}
θ
1
is located in Quadrant
\newline
IV, and
cos
(
θ
1
)
=
9
19
\cos \left(\theta_{1}\right)=\frac{9}{19}
cos
(
θ
1
)
=
19
9
.
\newline
What is the value of
sin
(
θ
1
)
\sin \left(\theta_{1}\right)
sin
(
θ
1
)
?
\newline
Express your answer exactly.
\newline
sin
(
θ
1
)
=
\sin \left(\theta_{1}\right)=
sin
(
θ
1
)
=
Get tutor help
The angle
θ
1
\theta_{1}
θ
1
is located in Quadrant IV, and
sin
(
θ
1
)
=
−
13
85
\sin \left(\theta_{1}\right)=-\frac{13}{85}
sin
(
θ
1
)
=
−
85
13
.
\newline
What is the value of
cos
(
θ
1
)
\cos \left(\theta_{1}\right)
cos
(
θ
1
)
? Express your answer exactly.
\newline
cos
(
θ
1
)
=
\cos \left(\theta_{1}\right)=
cos
(
θ
1
)
=
Get tutor help
The angle
θ
1
\theta_{1}
θ
1
is located in Quadrant III, and
sin
(
θ
1
)
=
−
12
13
\sin \left(\theta_{1}\right)=-\frac{12}{13}
sin
(
θ
1
)
=
−
13
12
.
\newline
What is the value of
cos
(
θ
1
)
\cos \left(\theta_{1}\right)
cos
(
θ
1
)
? Express your answer exactly.
\newline
cos
(
θ
1
)
=
\cos \left(\theta_{1}\right)=
cos
(
θ
1
)
=
Get tutor help
The angle
θ
1
\theta_{1}
θ
1
is located in Quadrant II, and
sin
(
θ
1
)
=
9
41
\sin \left(\theta_{1}\right)=\frac{9}{41}
sin
(
θ
1
)
=
41
9
.
\newline
What is the value of
cos
(
θ
1
)
\cos \left(\theta_{1}\right)
cos
(
θ
1
)
? Express your answer exactly.
\newline
cos
(
θ
1
)
=
\cos \left(\theta_{1}\right)=
cos
(
θ
1
)
=
Get tutor help
The angle
θ
1
\theta_{1}
θ
1
is located in Quadrant I, and
sin
(
θ
1
)
=
17
20
\sin \left(\theta_{1}\right)=\frac{17}{20}
sin
(
θ
1
)
=
20
17
.
\newline
What is the value of
cos
(
θ
1
)
\cos \left(\theta_{1}\right)
cos
(
θ
1
)
? Express your answer exactly.
\newline
cos
(
θ
1
)
=
\cos \left(\theta_{1}\right)=
cos
(
θ
1
)
=
Get tutor help
The angle
θ
1
\theta_{1}
θ
1
is located in Quadrant III, and
sin
(
θ
1
)
=
−
3
2
\sin \left(\theta_{1}\right)=-\frac{\sqrt{3}}{2}
sin
(
θ
1
)
=
−
2
3
.
\newline
What is the value of
cos
(
θ
1
)
\cos \left(\theta_{1}\right)
cos
(
θ
1
)
? Express your answer exactly.
\newline
cos
(
θ
1
)
=
\cos \left(\theta_{1}\right)=
cos
(
θ
1
)
=
Get tutor help
The angle
θ
1
\theta_{1}
θ
1
is located in Quadrant
\newline
IV, and
sin
(
θ
1
)
=
−
10
13
\sin \left(\theta_{1}\right)=-\frac{10}{13}
sin
(
θ
1
)
=
−
13
10
.
\newline
What is the value of
cos
(
θ
1
)
\cos \left(\theta_{1}\right)
cos
(
θ
1
)
?
\newline
Express your answer exactly.
\newline
cos
(
θ
1
)
=
\cos \left(\theta_{1}\right)=
cos
(
θ
1
)
=
Get tutor help
The angle
θ
1
\theta_{1}
θ
1
is located in Quadrant III, and
cos
(
θ
1
)
=
−
13
30
\cos \left(\theta_{1}\right)=-\frac{13}{30}
cos
(
θ
1
)
=
−
30
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
)
=
Get tutor help
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