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Math Problems
Algebra 2
Sin, cos, and tan of special angles
Determine the value of
y
y
y
, if
x
x
x
is
−
1
-1
−
1
.
\newline
y
=
46
x
−
1
y=\frac{46}{x-1}
y
=
x
−
1
46
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
8
-8
−
8
.
\newline
y
=
27
x
+
11
y=\frac{27}{x+11}
y
=
x
+
11
27
\newline
Answer:
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sin
u
cos
2
u
cos
3
u
\frac{\sin u \cos 2 u}{\cos ^{3} u}
c
o
s
3
u
s
i
n
u
c
o
s
2
u
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sin
2
u
cos
2
u
\frac{\sin ^{2} u}{\cos ^{2} u}
c
o
s
2
u
s
i
n
2
u
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Question
\newline
Watd
\newline
For which values of
x
\mathrm{x}
x
is the expression undefined?
\newline
3
x
−
12
x
2
−
25
\frac{3 x-12}{x^{2}-25}
x
2
−
25
3
x
−
12
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Find all horizontal asymptotes of the following function.
\newline
f
(
x
)
=
x
−
4
10
x
2
−
56
x
+
64
f(x)=\frac{x-4}{10 x^{2}-56 x+64}
f
(
x
)
=
10
x
2
−
56
x
+
64
x
−
4
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Solve the differential equation
d
y
d
x
=
−
e
x
8
\frac{d y}{d x}=-\frac{e^{x}}{8}
d
x
d
y
=
−
8
e
x
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Fully simplify using only positive exponents.
\newline
30
x
y
8
10
x
7
y
8
\frac{30 x y^{8}}{10 x^{7} y^{8}}
10
x
7
y
8
30
x
y
8
\newline
Answer:
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Factor the expression completely.
\newline
y
5
+
x
2
y
5
y^{5}+x^{2} y^{5}
y
5
+
x
2
y
5
\newline
Answer:
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Factor the expression completely.
\newline
x
y
+
x
5
y
5
x y+x^{5} y^{5}
x
y
+
x
5
y
5
\newline
Answer:
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Find the derivative of
y
y
y
with respect to
θ
\theta
θ
:
y
=
(
5
−
5
θ
)
tanh
−
1
(
θ
)
y = (5 - 5\theta)\tanh^{-1}(\theta)
y
=
(
5
−
5
θ
)
tanh
−
1
(
θ
)
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Evaluate. Write your answer as a whole number or as a simplified fraction.
\newline
2
2
⋅
2
2
=
□
2^{2} \cdot 2^{2} = \square
2
2
⋅
2
2
=
□
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Given the function
y
=
x
−
x
sin
x
y=x-x\sin x
y
=
x
−
x
sin
x
, find
d
y
d
x
\frac{dy}{dx}
d
x
d
y
in any form.
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Find
d
y
d
x
\frac{dy}{dx}
d
x
d
y
.
4
x
y
=
sin
(
x
+
y
)
4xy=\sin(x+y)
4
x
y
=
sin
(
x
+
y
)
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Find the derivative of
y
y
y
with
y
=
(
5
−
5
θ
)
tanh
−
1
(
θ
)
y=(5-5\theta)\tanh^{-1}(\theta)
y
=
(
5
−
5
θ
)
tanh
−
1
(
θ
)
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If
y
2
cos
(
1
x
)
=
a
2
y^{2}\cos\left(\frac{1}{x}\right)=a^{2}
y
2
cos
(
x
1
)
=
a
2
, then find
d
y
d
x
\frac{dy}{dx}
d
x
d
y
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Solve the differential equation.
\newline
d
y
d
x
=
6
x
y
\frac{dy}{dx}=6\sqrt{xy}
d
x
d
y
=
6
x
y
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(i)
\newline
lim
x
→
0
(
tan
2
x
−
sin
2
x
x
3
)
\lim_{x \to 0} \left( \frac{\tan 2x - \sin 2x}{x^{3}} \right)
lim
x
→
0
(
x
3
t
a
n
2
x
−
s
i
n
2
x
)
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Determine the value of
y
y
y
, if
x
x
x
is
10
10
10
.
\newline
y
=
46
x
−
8
y=\frac{46}{x-8}
y
=
x
−
8
46
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Find the derivative of the function.
\newline
g
(
t
)
=
1
(
7
t
+
1
)
6
g(t)=\frac{1}{(7t+1)^{6}}
g
(
t
)
=
(
7
t
+
1
)
6
1
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Evaluate. Write your answer in simplified, rationalized form. Do not round.
\newline
cos
9
0
∘
=
\cos 90^\circ =
cos
9
0
∘
=
____
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