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Math Problems
Algebra 2
Sin, cos, and tan of special angles
What is the measure of
∠
A
\angle A
∠
A
to the nearest degree?
\newline
3
0
∘
30^{\circ}
3
0
∘
\newline
4
5
∘
45^{\circ}
4
5
∘
\newline
15
0
∘
150^{\circ}
15
0
∘
\newline
18
0
∘
180^{\circ}
18
0
∘
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Given the function
y
=
x
4
−
x
4
y=\frac{x}{4-x^{4}}
y
=
4
−
x
4
x
, find
d
y
d
x
\frac{dy}{dx}
d
x
d
y
in simplified form.
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Simplify:
sec
2
θ
sec
2
θ
−
1
=
csc
2
θ
\frac{\sec^{2}\theta}{\sec^{2}\theta-1}=\csc^{2}\theta
s
e
c
2
θ
−
1
s
e
c
2
θ
=
csc
2
θ
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Which equation has both
1
4
\frac{1}{4}
4
1
and
−
1
4
-\frac{1}{4}
−
4
1
as possible values of
x
x
x
? Select all that apply.
\newline
Multi-select Choices:
\newline
(A)
x
2
=
1
2
x^2 = \frac{1}{2}
x
2
=
2
1
\newline
(B)
x
3
=
1
2
x^3 = \frac{1}{2}
x
3
=
2
1
\newline
(C)
x
2
=
1
16
x^2 = \frac{1}{16}
x
2
=
16
1
\newline
(D)
x
3
=
1
16
x^3 = \frac{1}{16}
x
3
=
16
1
\newline
(E)
x
2
=
1
64
x^2 = \frac{1}{64}
x
2
=
64
1
\newline
(F)
x
3
=
1
64
x^3 = \frac{1}{64}
x
3
=
64
1
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What could be the value of
x
x
x
in the following equation? Select all that apply.
\newline
x
2
=
49
x^2 = 49
x
2
=
49
\newline
Multi-select Choices:
\newline
(A)
7
7
7
\newline
(B)
−
7
-7
−
7
\newline
(C)
49
\sqrt{49}
49
\newline
(D)
−
49
-\sqrt{49}
−
49
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Evaluate the integral
\newline
∫
cos
3
(
x
)
sin
(
x
)
d
x
=
\int \cos^{3}(x)\sin(x)dx =
∫
cos
3
(
x
)
sin
(
x
)
d
x
=
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Evaluate the following expression.
\newline
6
6
6
⋅
\cdot
⋅
2
2
2
+
6
4
=
+6^{4}=
+
6
4
=
□
\square
□
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a
2
+
1
=
0
a^{2}+1=0
a
2
+
1
=
0
\newline
How many distinct real solutions does the given equation have?
\newline
□
\square
□
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a)
12
x
y
40
x
2
\frac{12 x y}{40 x^{2}}
40
x
2
12
x
y
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Evaluate. Write your answer as a whole number or as a simplified fraction.
\newline
3
2
3^{2}
3
2
⋅
\cdot
⋅
3
2
3^{2}
3
2
=
□
\Box
□
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If
a
=
3
+
5
2
a=\frac{3+\sqrt{5}}{2}
a
=
2
3
+
5
, then find the value of
a
2
+
1
a
2
a^{2}+\frac{1}{a^{2}}
a
2
+
a
2
1
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Find
n
n
n
.
\newline
9
n
+
9
n
+
9
n
=
3
99
9^{n}+9^{n}+9^{n}=3^{99}
9
n
+
9
n
+
9
n
=
3
99
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Expand.
\newline
If necessary, combine like terms.
\newline
(
7
x
−
1
)
2
=
(7 x-1)^{2}=
(
7
x
−
1
)
2
=
\newline
□
\square
□
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Rearrange
y
=
2
(
x
−
a
)
x
y=\frac{2(x-a)}{x}
y
=
x
2
(
x
−
a
)
to make
x
x
x
the subject
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tan
α
+
cot
α
tan
α
−
cot
α
=
1
2
sin
2
α
−
1
\frac{\tan \alpha+\cot \alpha}{\tan \alpha-\cot \alpha}=\frac{1}{2 \sin ^{2} \alpha-1}
t
a
n
α
−
c
o
t
α
t
a
n
α
+
c
o
t
α
=
2
s
i
n
2
α
−
1
1
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https://www.bytelearn.com/b
2
2
2
c/referral?referralCode=MGb
7
7
7
mH
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0
∘
≤
θ
≤
18
0
∘
0^{\circ} \leq \theta \leq 180^{\circ}
0
∘
≤
θ
≤
18
0
∘
. Find the value of
θ
\theta
θ
in degrees.
\newline
cos
(
θ
)
=
−
1
\cos (\theta)=-1
cos
(
θ
)
=
−
1
\newline
Write your answer in simplified, rationalized form. Do not round.
\newline
θ
=
□
∘
\theta=\square^{\circ}
θ
=
□
∘
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Find
sec
θ
\sec \theta
sec
θ
if
sin
θ
=
3
13
13
\sin \theta=\frac{3 \sqrt{13}}{13}
sin
θ
=
13
3
13
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In
△
L
M
N
,
M
N
‾
≅
L
M
‾
\triangle L M N, \overline{M N} \cong \overline{L M}
△
L
MN
,
MN
≅
L
M
and
m
∠
L
=
7
6
∘
\mathrm{m} \angle L=76^{\circ}
m
∠
L
=
7
6
∘
. Find
m
∠
M
\mathrm{m} \angle M
m
∠
M
.
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cos
4
α
−
sin
4
α
=
cos
2
α
\cos ^{4} \alpha-\sin ^{4} \alpha=\cos 2 \alpha
cos
4
α
−
sin
4
α
=
cos
2
α
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cot
x
2
=
a
⇒
sin
x
=
\cot \frac{x}{2}=a \Rightarrow \sin x=
cot
2
x
=
a
⇒
sin
x
=
?
\newline
(cot: ctg: cotangent)
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Identify the following exponential function as being growth or decay.
\newline
f
(
x
)
=
(
3
4
)
x
f(x)=\left(\frac{3}{4}\right)^{x}
f
(
x
)
=
(
4
3
)
x
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In
Δ
K
L
M
,
m
=
55
\Delta \mathrm{KLM}, m=55
Δ
KLM
,
m
=
55
inches,
l
=
49
l=49
l
=
49
inches and
∠
L
=
12
1
∘
\angle \mathrm{L}=121^{\circ}
∠
L
=
12
1
∘
. Find all possible values of
∠
M
\angle \mathrm{M}
∠
M
, to the nearest degree.
\newline
Answer:
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In
Δ
K
L
M
,
m
=
98
\Delta \mathrm{KLM}, m=98
Δ
KLM
,
m
=
98
inches,
l
=
95
l=95
l
=
95
inches and
∠
L
=
11
4
∘
\angle \mathrm{L}=114^{\circ}
∠
L
=
11
4
∘
. Find all possible values of
∠
M
\angle \mathrm{M}
∠
M
, to the nearest degree.
\newline
Answer:
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Express as a function of a DIFFERENT angle,
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
.
\newline
cos
(
22
0
∘
)
\cos \left(220^{\circ}\right)
cos
(
22
0
∘
)
\newline
cos
(
□
∘
)
\cos \left(\square^{\circ}\right)
cos
(
□
∘
)
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Express as a function of a DIFFERENT angle,
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
.
\newline
cos
(
12
6
∘
)
\cos \left(126^{\circ}\right)
cos
(
12
6
∘
)
\newline
cos
(
□
∘
)
\cos \left(\square^{\circ}\right)
cos
(
□
∘
)
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Express as a function of a DIFFERENT angle,
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
.
\newline
cos
(
11
0
∘
)
\cos \left(110^{\circ}\right)
cos
(
11
0
∘
)
\newline
cos
(
□
∘
)
\cos \left(\square^{\circ}\right)
cos
(
□
∘
)
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Express as a function of a DIFFERENT angle,
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
.
\newline
sin
(
7
1
∘
)
\sin \left(71^{\circ}\right)
sin
(
7
1
∘
)
\newline
sin
(
□
∘
)
\sin \left(\square^{\circ}\right)
sin
(
□
∘
)
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Express as a function of a DIFFERENT angle,
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
.
\newline
tan
(
34
9
∘
)
\tan \left(349^{\circ}\right)
tan
(
34
9
∘
)
\newline
tan
(
□
∘
)
\tan \left(\square^{\circ}\right)
tan
(
□
∘
)
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Express as a function of a DIFFERENT angle,
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
.
\newline
cos
(
7
4
∘
)
\cos \left(74^{\circ}\right)
cos
(
7
4
∘
)
\newline
cos
(
□
∘
)
\cos \left(\square^{\circ}\right)
cos
(
□
∘
)
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Express as a function of a DIFFERENT angle,
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
.
\newline
cos
(
12
3
∘
)
\cos \left(123^{\circ}\right)
cos
(
12
3
∘
)
\newline
cos
(
□
∘
)
\cos \left(\square^{\circ}\right)
cos
(
□
∘
)
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Express as a function of a DIFFERENT angle,
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
.
\newline
sin
(
12
8
∘
)
\sin \left(128^{\circ}\right)
sin
(
12
8
∘
)
\newline
sin
(
□
∘
)
\sin \left(\square^{\circ}\right)
sin
(
□
∘
)
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Express as a function of a DIFFERENT angle,
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
.
\newline
cos
(
8
8
∘
)
\cos \left(88^{\circ}\right)
cos
(
8
8
∘
)
\newline
cos
(
□
∘
)
\cos \left(\square^{\circ}\right)
cos
(
□
∘
)
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Express as a function of a DIFFERENT angle,
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
.
\newline
cos
(
5
∘
)
\cos \left(5^{\circ}\right)
cos
(
5
∘
)
\newline
cos
(
□
∘
)
\cos \left(\square^{\circ}\right)
cos
(
□
∘
)
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y
4
−
2
x
=
5
y^4-2x=5
y
4
−
2
x
=
5
, find
d
2
y
d
2
x
\frac{d^2y}{d^2x}
d
2
x
d
2
y
at
(
−
2
,
1
)
(-2,1)
(
−
2
,
1
)
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The average value of
csc
2
x
\csc^2 x
csc
2
x
over the interval from
x
=
π
6
x=\frac{\pi}{6}
x
=
6
π
to
x
=
π
4
x=\frac{\pi}{4}
x
=
4
π
is
\newline
(A)
3
3
π
\frac{3\sqrt{3}}{\pi}
π
3
3
\newline
(B)
3
π
\frac{\sqrt{3}}{\pi}
π
3
\newline
(C)
12
π
(
3
−
1
)
\frac{12}{\pi}(\sqrt{3}-1)
π
12
(
3
−
1
)
\newline
(D)
3
(
3
−
1
)
3(\sqrt{3}-1)
3
(
3
−
1
)
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What expression is equivalent to
(
x
y
7
z
3
)
6
\left(x y^{7} z^{3}\right)^{6}
(
x
y
7
z
3
)
6
?
\newline
Enter numbers in the boxes provided.
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∫
e
arcsin
x
d
x
\int e^{\arcsin x}\,dx
∫
e
a
r
c
s
i
n
x
d
x
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∫
arcsin
t
d
t
\int \arcsin t \, dt
∫
arcsin
t
d
t
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If
u
=
e
x
y
z
u=e^{xyz}
u
=
e
x
yz
find
∂
3
u
∂
x
∂
y
∂
z
\frac{\partial^{3}u}{\partial x \partial y \partial z}
∂
x
∂
y
∂
z
∂
3
u
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Write an expression that is equivalent to
3
k
−
18.
3k-18.
3
k
−
18.
\newline
3
k
−
18
=
□
(
k
−
?
)
3k-18=\square(k-\ ?)
3
k
−
18
=
□
(
k
−
?)
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Find
d
y
d
x
\frac{dy}{dx}
d
x
d
y
, if
y
=
(
−
5
x
2
−
3
)
−
4
y=(-5x^{2}-3)^{-4}
y
=
(
−
5
x
2
−
3
)
−
4
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Expand.
\newline
If necessary, combine like terms.
\newline
(
5
x
−
6
)
2
=
□
(5x-6)^2=\square
(
5
x
−
6
)
2
=
□
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Simplify the expression completely if possible.
\newline
4
x
2
8
x
2
+
48
x
\frac{4 x^{2}}{8 x^{2}+48 x}
8
x
2
+
48
x
4
x
2
\newline
Answer:
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Simplify the expression completely if possible.
\newline
5
x
3
15
x
2
−
30
x
\frac{5 x^{3}}{15 x^{2}-30 x}
15
x
2
−
30
x
5
x
3
\newline
Answer:
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Simplify the expression completely if possible.
\newline
6
x
2
+
24
x
6
x
\frac{6 x^{2}+24 x}{6 x}
6
x
6
x
2
+
24
x
\newline
Answer:
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Simplify the expression completely if possible.
\newline
6
x
2
+
42
x
18
x
2
\frac{6 x^{2}+42 x}{18 x^{2}}
18
x
2
6
x
2
+
42
x
\newline
Answer:
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Simplify the expression completely if possible.
\newline
16
x
2
−
64
x
8
x
3
\frac{16 x^{2}-64 x}{8 x^{3}}
8
x
3
16
x
2
−
64
x
\newline
Answer:
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z
=
5
−
3
i
z=5-3i
z
=
5
−
3
i
\newline
Find the angle
θ
\theta
θ
(in degrees) that
z
z
z
makes in the complex plane.
\newline
Round your answer, if necessary, to the nearest tenth. Express
θ
\theta
θ
between
\newline
−
18
0
∘
-180^\circ
−
18
0
∘
and
18
0
∘
180^\circ
18
0
∘
.
\newline
θ
=
□
∘
\theta=\square^\circ
θ
=
□
∘
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Solve the equation. Check your solution
\newline
11
−
7
a
=
−
9
a
+
8
∘
11-7 a=-9 a+8^{\circ}
11
−
7
a
=
−
9
a
+
8
∘
\newline
The solution set is
{
□
}
\{\square\}
{
□
}
. Simplify your answer
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