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Math Problems
Algebra 2
Solve trigonometric equations I
Find all solutions with
−
9
0
∘
≤
θ
≤
9
0
∘
-90^\circ \leq \theta \leq 90^\circ
−
9
0
∘
≤
θ
≤
9
0
∘
. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.
\newline
csc
(
θ
)
=
−
1
\csc(\theta) = -1
csc
(
θ
)
=
−
1
\newline
_
_
_
_
∘
\_\_\_\_\,^\circ
____
∘
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Find all solutions with
−
9
0
∘
≤
θ
≤
9
0
∘
-90^\circ \leq \theta \leq 90^\circ
−
9
0
∘
≤
θ
≤
9
0
∘
. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.
\newline
sin
(
θ
)
=
−
1
\sin (\theta) = -1
sin
(
θ
)
=
−
1
\newline
_
_
_
_
∘
\_\_\_\_\,^\circ
____
∘
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Find all solutions with
−
9
0
∘
<
θ
<
9
0
∘
-90^\circ < \theta < 90^\circ
−
9
0
∘
<
θ
<
9
0
∘
. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.
\newline
tan
(
θ
)
=
0
\tan (\theta) = 0
tan
(
θ
)
=
0
\newline
_
_
_
_
∘
\_\_\_\_\,^\circ
____
∘
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Find all solutions with
−
9
0
∘
<
θ
<
9
0
∘
-90^\circ < \theta < 90^\circ
−
9
0
∘
<
θ
<
9
0
∘
. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.
\newline
tan
(
θ
)
=
1
\tan (\theta) = 1
tan
(
θ
)
=
1
\newline
_
_
_
_
∘
\_\_\_\_\,^\circ
____
∘
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Find all solutions with
0
∘
≤
θ
≤
18
0
∘
0^\circ \leq \theta \leq 180^\circ
0
∘
≤
θ
≤
18
0
∘
. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.
\newline
cos
(
θ
)
=
1
2
\cos (\theta) = \frac{1}{2}
cos
(
θ
)
=
2
1
\newline
_
_
_
_
∘
\_\_\_\_\,^\circ
____
∘
Get tutor help
Find all solutions with
−
9
0
∘
≤
θ
≤
9
0
∘
-90^\circ \leq \theta \leq 90^\circ
−
9
0
∘
≤
θ
≤
9
0
∘
. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.
\newline
sin
(
θ
)
=
1
\sin (\theta) = 1
sin
(
θ
)
=
1
\newline
_
_
_
_
∘
\_\_\_\_\,^\circ
____
∘
Get tutor help
Find all solutions with
−
9
0
∘
<
θ
<
9
0
∘
-90^\circ < \theta < 90^\circ
−
9
0
∘
<
θ
<
9
0
∘
. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.
\newline
tan
(
θ
)
=
−
1
\tan (\theta) = -1
tan
(
θ
)
=
−
1
\newline
_
_
_
_
∘
\_\_\_\_\,^\circ
____
∘
Get tutor help
Find all solutions with
0
∘
≤
θ
≤
18
0
∘
0^\circ \leq \theta \leq 180^\circ
0
∘
≤
θ
≤
18
0
∘
. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.
\newline
cos
(
θ
)
=
0
\cos (\theta) = 0
cos
(
θ
)
=
0
\newline
_
_
_
_
∘
\_\_\_\_\,^\circ
____
∘
Get tutor help
Find all solutions with
−
90
°
≤
θ
≤
90
°
-90° \leq \theta \leq 90°
−
90°
≤
θ
≤
90°
. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.
\newline
sin
(
θ
)
=
0
\sin (\theta) = 0
sin
(
θ
)
=
0
\newline
_
_
_
_
°
\_\_\_\_°
____°
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Find all solutions with
−
90
°
≤
θ
≤
90
°
-90° \leq \theta \leq 90°
−
90°
≤
θ
≤
90°
. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.
\newline
sin
(
θ
)
=
1
2
\sin (\theta) = \frac{1}{2}
sin
(
θ
)
=
2
1
\newline
___°
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How many solutions does the system of equations below have?
\newline
y
=
x
−
5
y = x - 5
y
=
x
−
5
\newline
y
=
−
7
5
x
+
10
3
y = -\frac{7}{5}x + \frac{10}{3}
y
=
−
5
7
x
+
3
10
\newline
Choices:
\newline
(A)no solution
\newline
(B)one solution
\newline
(C)infinitely many solutions
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How many solutions does the system of equations below have?
\newline
y
=
−
4
x
+
2
y = -4x + 2
y
=
−
4
x
+
2
\newline
y
=
−
4
x
+
2
y = -4x + 2
y
=
−
4
x
+
2
\newline
Choices:
\newline
(A)no solution
\newline
(B)one solution
\newline
(C)infinitely many solutions
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How many solutions does the system of equations below have?
\newline
y
=
−
3
x
+
3
y = -3x + 3
y
=
−
3
x
+
3
\newline
y
=
−
3
x
−
7
5
y = -3x - \frac{7}{5}
y
=
−
3
x
−
5
7
\newline
Choices:
\newline
(A)no solution
\newline
(B)one solution
\newline
(C)infinitely many solutions
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Line
s
s
s
has an equation of
y
=
8
x
+
7
y=8 x+7
y
=
8
x
+
7
. Line
t
t
t
is perpendicular to line
s
s
s
and passes through
(
−
8
,
−
2
)
(-8,-2)
(
−
8
,
−
2
)
. What is the equation of line
t
t
t
?
\newline
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
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What are the critical points for the plane curve defined by the equations
x
(
t
)
=
−
sin
(
3
t
)
,
y
(
t
)
=
5
t
x(t)=-\sin (3 t), y(t)=5 t
x
(
t
)
=
−
sin
(
3
t
)
,
y
(
t
)
=
5
t
, and
0
≤
t
<
π
0 \leq t<\pi
0
≤
t
<
π
? Write your answer as a list of values of
t
t
t
, separated by commas. For example, if you found
t
=
1
t=1
t
=
1
or
t
=
2
t=2
t
=
2
, you would enter
1
1
1
,
2
2
2
.
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The equation
\newline
−
x
−
2
y
=
0
-x-2y=0
−
x
−
2
y
=
0
is graphed in the
\newline
x
y
xy
x
y
-plane. Which of the following is a true statement about the graph?
\newline
Choose
1
1
1
answer:
\newline
(A) The graph goes through the point
\newline
(
−
1
,
2
)
(-1,2)
(
−
1
,
2
)
.
\newline
(B) The graph has a slope of
2
2
2
.
\newline
(C) The graph goes through the point
\newline
(
0
,
0
)
(0,0)
(
0
,
0
)
.
\newline
(D) The graph has a slope of
\newline
1
2
\frac{1}{2}
2
1
.
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Kajal tried to solve the differential equation
d
y
d
x
=
−
x
2
y
2
\frac{d y}{d x}=-x^{2} y^{2}
d
x
d
y
=
−
x
2
y
2
. This is her work:
\newline
d
y
d
x
=
−
x
2
y
2
\frac{d y}{d x}=-x^{2} y^{2}
d
x
d
y
=
−
x
2
y
2
\newline
Step
1
1
1
:
∫
−
y
−
2
d
y
=
∫
x
2
d
x
\quad \int-y^{-2} d y=\int x^{2} d x
∫
−
y
−
2
d
y
=
∫
x
2
d
x
\newline
Step
2
2
2
:
y
−
1
=
x
3
3
+
C
\quad y^{-1}=\frac{x^{3}}{3}+C
y
−
1
=
3
x
3
+
C
\newline
Step
3
3
3
:
y
=
3
x
3
+
C
\quad y=\frac{3}{x^{3}}+C
y
=
x
3
3
+
C
\newline
Is Kajal's work correct? If not, what is her mistake?
\newline
Choose
1
1
1
answer:
\newline
(A) Kajal's work is correct.
\newline
(B) Step
1
1
1
is incorrect. The separation of variables wasn't done correctly.
\newline
(C) Step
2
2
2
is incorrect. Kajal didn't integrate
x
2
x^{2}
x
2
correctly.
\newline
(D) Step
3
3
3
is incorrect. Kajal didn't take the reciprocal of
x
3
3
+
C
\frac{x^{3}}{3}+C
3
x
3
+
C
correctly.
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Evaluate. Write your answer in simplified, rationalized form. Do not round.
\newline
cot
3
0
∘
=
\cot 30^\circ =
cot
3
0
∘
=
______
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Find all solutions with
−
9
0
∘
≤
θ
≤
9
0
∘
-90^\circ \leq \theta \leq 90^\circ
−
9
0
∘
≤
θ
≤
9
0
∘
. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.
\newline
csc
(
θ
)
=
−
1
\csc(\theta) = -1
csc
(
θ
)
=
−
1
\newline
_
_
_
_
∘
\_\_\_\_\,^\circ
____
∘
Get tutor help
Find all solutions with
0
∘
≤
θ
≤
18
0
∘
0^\circ \leq \theta \leq 180^\circ
0
∘
≤
θ
≤
18
0
∘
. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.
\newline
cos
(
θ
)
=
−
1
\cos(\theta) = -1
cos
(
θ
)
=
−
1
\newline
‾
∘
\underline{\hspace{2em}}^\circ
∘
Get tutor help
