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Math Problems
Algebra 2
Quadrants
Find
tan
(
2
A
)
\tan (2 A)
tan
(
2
A
)
, if
tan
(
A
)
=
84
13
\tan (A)=\frac{84}{13}
tan
(
A
)
=
13
84
, and
A
A
A
is in quadrant
1
1
1
.
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If
x
<
0
x < 0
x
<
0
and
y
<
0
y < 0
y
<
0
, where is the point
(
x
,
y
)
(x, y)
(
x
,
y
)
located?
\newline
Choices:
\newline
(A) Quadrant I
\newline
(B) Quadrant II
\newline
(C) Quadrant III
\newline
(D) Quadrant IV
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If
x
>
0
x > 0
x
>
0
and
y
<
0
y < 0
y
<
0
, where is the point
(
x
,
y
)
(x, y)
(
x
,
y
)
located?
\newline
Choices:
\newline
(A) Quadrant I
\newline
(B) Quadrant II
\newline
(C) Quadrant III
\newline
(D) Quadrant IV
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If
x
>
0
x > 0
x
>
0
and
y
>
0
y > 0
y
>
0
, where is the point
(
x
,
y
)
(x, y)
(
x
,
y
)
located?
\newline
Choices:
\newline
(A)Quadrant I
\newline
(B)Quadrant II
\newline
(C)Quadrant III
\newline
(D)Quadrant IV
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If
x
<
0
x < 0
x
<
0
and
y
>
0
y > 0
y
>
0
, where is the point
(
x
,
y
)
(x, y)
(
x
,
y
)
located?
\newline
Choices:
\newline
(A) Quadrant I
\newline
(B) Quadrant II
\newline
(C) Quadrant III
\newline
(D) Quadrant IV
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Example \#
2
2
2
: The angle
θ
\theta
θ
is in standard position and
tan
θ
=
−
4
3
\tan \theta=-\frac{4}{3}
tan
θ
=
−
3
4
\newline
a) In which quadrants could the terminal arm of the angle lie?
\newline
Quadrant
3
3
3
\newline
b) draw a diagram for each case
\newline
x
2
+
y
2
=
c
2
x^{2}+y^{2}=c^{2}
x
2
+
y
2
=
c
2
\newline
c) determine all possible values for
θ
\theta
θ
.
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If
sin
A
=
45
53
\sin A=\frac{45}{53}
sin
A
=
53
45
and
cos
B
=
12
13
\cos B=\frac{12}{13}
cos
B
=
13
12
and angles A and B are in Quadrant I, find the value of
tan
(
A
+
B
)
\tan (A+B)
tan
(
A
+
B
)
.
\newline
Answer:
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If
cos
A
=
60
61
\cos A=\frac{60}{61}
cos
A
=
61
60
and
tan
B
=
8
15
\tan B=\frac{8}{15}
tan
B
=
15
8
and angles A and B are in Quadrant I, find the value of
tan
(
A
+
B
)
\tan (A+B)
tan
(
A
+
B
)
.
\newline
Answer:
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In which quadrant does
θ
\theta
θ
lie if the following statements are true:
\newline
tan
θ
<
0
and
sin
θ
<
0
\tan \theta<0 \text { and } \sin \theta<0
tan
θ
<
0
and
sin
θ
<
0
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In which quadrant does the point
(
8
,
7
)
(8,7)
(
8
,
7
)
lie?
\newline
Quadrant I
\newline
Quadrant II
\newline
Quadrant III
\newline
Quadrant IV
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In which quadrant does the point
(
1
,
3
)
(1,3)
(
1
,
3
)
lie?
\newline
Quadrant
1
1
1
\newline
Quadrant
2
2
2
\newline
Quadrant
3
3
3
\newline
Quadrant
4
4
4
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In which quadrant does the point
(
−
3
,
6
)
(-3,6)
(
−
3
,
6
)
lie?
\newline
Quadrant
1
1
1
\newline
Quadrant
2
2
2
\newline
Quadrant
3
3
3
\newline
Quadrant
4
4
4
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In which quadrant does the point
(
−
3
,
4
)
(-3,4)
(
−
3
,
4
)
lie?
\newline
Quadrant
1
1
1
\newline
Quadrant
2
2
2
\newline
Quadrant
3
3
3
\newline
Quadrant
4
4
4
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In which quadrant does the point
(
−
4
,
8
)
(-4,8)
(
−
4
,
8
)
lie?
\newline
Quadrant
1
1
1
\newline
Quadrant
2
2
2
\newline
Quadrant
3
3
3
\newline
Quadrant
4
4
4
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In which quadrant does the point
(
2
,
−
6
)
(2,-6)
(
2
,
−
6
)
lie?
\newline
1
1
1
st Quadrant
\newline
2
2
2
nd Quadrant
\newline
3
3
3
rd Quadrant
\newline
4
4
4
th Quadrant
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In which quadrant does the point
(
−
5
,
3
)
(-5,3)
(
−
5
,
3
)
lie?
\newline
1
1
1
st Quadrant
\newline
2
2
2
nd Quadrant
\newline
3
3
3
rd Quadrant
\newline
4
4
4
th Quadrant
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In which quadrant does the point
(
−
4
,
4
)
(-4,4)
(
−
4
,
4
)
lie?
\newline
Quadrant
1
1
1
\newline
Quadrant
2
2
2
\newline
Quadrant
3
3
3
\newline
Quadrant
4
4
4
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In which quadrant does the point
(
6
,
1
)
(6,1)
(
6
,
1
)
lie?
\newline
Quadrant
1
1
1
\newline
Quadrant
2
2
2
\newline
Quadrant
3
3
3
\newline
Quadrant
4
4
4
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In which quadrant does the point
(
−
8
,
−
6
)
(-8,-6)
(
−
8
,
−
6
)
lie?
\newline
Quadrant
1
1
1
\newline
Quadrant
2
2
2
\newline
Quadrant
3
3
3
\newline
Quadrant
4
4
4
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In which quadrant does the point
(
−
8
,
−
7
)
(-8,-7)
(
−
8
,
−
7
)
lie?
\newline
Quadrant
1
1
1
\newline
Quadrant
2
2
2
\newline
Quadrant
3
3
3
\newline
Quadrant
4
4
4
Get tutor help
In which quadrant does the point
(
−
8
,
7
)
(-8,7)
(
−
8
,
7
)
lie?
\newline
Quadrant
1
1
1
\newline
Quadrant
2
2
2
\newline
Quadrant
3
3
3
\newline
Quadrant
4
4
4
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In which quadrant does the point
(
−
3
,
4
)
(-3,4)
(
−
3
,
4
)
lie?
\newline
Quadrant I
\newline
Quadrant II
\newline
Quadrant III
\newline
Quadrant IV
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Find
sin
2
x
,
cos
2
x
\sin 2 x, \cos 2 x
sin
2
x
,
cos
2
x
, and
tan
2
x
\tan 2 x
tan
2
x
if
cos
x
=
3
5
\cos x=\frac{3}{5}
cos
x
=
5
3
and
x
x
x
terminates in quadrant
I
I
I
.
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Objective A: Solve a System of Three Linear Equations in Three Variables
\newline
YOUR TURN
\newline
\#\#
1
1
1
\newline
Solve the following system of equations.
\newline
{
2
x
+
2
y
+
z
=
−
9
−
x
+
y
+
4
z
=
−
7
x
+
y
+
2
z
=
−
9
\left\{\begin{array}{r} 2 x+2 y+z=-9 \\ -x+y+4 z=-7 \\ x+y+2 z=-9 \end{array}\right.
⎩
⎨
⎧
2
x
+
2
y
+
z
=
−
9
−
x
+
y
+
4
z
=
−
7
x
+
y
+
2
z
=
−
9
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Question
\newline
Find an angle in each quadrant with a common reference angle with
16
5
∘
165^{\circ}
16
5
∘
, from
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
\newline
Answer Attempt
1
1
1
out of
2
2
2
\newline
Quadrant I: Quadrant II:
\newline
Quadrant III:
\newline
Quadrant IV:
\newline
Submit Answer
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Question
\newline
Show Examples
\newline
Find an angle in each quadrant with a common reference angle with
16
5
∘
165^{\circ}
16
5
∘
, from
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
\newline
Answer Attempt
1
1
1
out of
2
2
2
\newline
Quadrant I:
\newline
Quadrant II:
\newline
Quadrant III:
\newline
Quadrant IV:
\newline
Submit Answer
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Show Examples
\newline
Question
\newline
Find an angle in each quadrant with a common reference angle with
6
6
∘
66^{\circ}
6
6
∘
, from
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
\newline
Answer Attempt
1
1
1
out of
2
2
2
\newline
Quadrant I:
\newline
Quadrant II:
\newline
Quadrant III: Quadrant IV:
\newline
Submit Answer
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{
y
≥
−
1
3
x
+
3
y
>
3
4
x
−
1
\left\{\begin{array}{l} y \geq-\frac{1}{3} x+3 \\ y>\frac{3}{4} x-1 \end{array}\right.
{
y
≥
−
3
1
x
+
3
y
>
4
3
x
−
1
\newline
Which quadrants contain the solution to this system of inequalities?
\newline
A. quadrants I, II, and IV
\newline
B. quadrants I and II
\newline
C. quadrants II and III
\newline
D. quadrants I and IV
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If the system of inequalities
\newline
y
≤
−
3
x
−
4
y \leq -3x-4
y
≤
−
3
x
−
4
and
\newline
y
≤
3
x
+
8
y \leq 3x+8
y
≤
3
x
+
8
is graphed in the
\newline
x
y
xy
x
y
-plane, which quadrant contains no solutions to the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Quadrant I
\newline
(B) Quadrant II
\newline
(C) Quadrant III
\newline
(D) Quadrant IV
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