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Let’s check out your problem:
Simplify to a single trig function with no denominator.
\newline
sin
θ
tan
θ
\frac{\sin \theta}{\tan \theta}
tan
θ
sin
θ
\newline
Answer:
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Math Problems
Algebra 2
Simplify expressions using trigonometric identities
Full solution
Q.
Simplify to a single trig function with no denominator.
\newline
sin
θ
tan
θ
\frac{\sin \theta}{\tan \theta}
tan
θ
sin
θ
\newline
Answer:
Express
tan
(
θ
)
\tan(\theta)
tan
(
θ
)
:
Express
tan
(
θ
)
\tan(\theta)
tan
(
θ
)
in terms of
sin
(
θ
)
\sin(\theta)
sin
(
θ
)
and
cos
(
θ
)
\cos(\theta)
cos
(
θ
)
as
tan
(
θ
)
=
sin
(
θ
)
cos
(
θ
)
\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}
tan
(
θ
)
=
c
o
s
(
θ
)
s
i
n
(
θ
)
.
Substitute
tan
(
θ
)
\tan(\theta)
tan
(
θ
)
:
Substitute
tan
(
θ
)
\tan(\theta)
tan
(
θ
)
with
sin
(
θ
)
cos
(
θ
)
\frac{\sin(\theta)}{\cos(\theta)}
c
o
s
(
θ
)
s
i
n
(
θ
)
in the given expression to get
sin
(
θ
)
sin
(
θ
)
/
cos
(
θ
)
\frac{\sin(\theta)}{\sin(\theta)/\cos(\theta)}
s
i
n
(
θ
)
/
c
o
s
(
θ
)
s
i
n
(
θ
)
.
Simplify expression:
Simplify
(
sin
(
θ
)
)
/
(
sin
(
θ
)
/
cos
(
θ
)
)
(\sin(\theta))/(\sin(\theta)/\cos(\theta))
(
sin
(
θ
))
/
(
sin
(
θ
)
/
cos
(
θ
))
by multiplying the numerator and denominator by
cos
(
θ
)
\cos(\theta)
cos
(
θ
)
to get
(
sin
(
θ
)
⋅
cos
(
θ
)
)
/
sin
(
θ
)
(\sin(\theta) \cdot \cos(\theta))/\sin(\theta)
(
sin
(
θ
)
⋅
cos
(
θ
))
/
sin
(
θ
)
.
Cancel common terms:
Cancel out the common
sin
(
θ
)
\sin(\theta)
sin
(
θ
)
terms in the numerator and denominator to get
cos
(
θ
)
\cos(\theta)
cos
(
θ
)
.
More problems from Simplify expressions using trigonometric identities
Question
If
cos
(
θ
)
=
8
17
\cos(\theta)=\frac{8}{17}
cos
(
θ
)
=
17
8
and
0
∘
<
θ
<
9
0
∘
0^\circ<\theta<90^\circ
0
∘
<
θ
<
9
0
∘
, what is
sec
(
θ
)
\sec(\theta)
sec
(
θ
)
? Write your answer in simplified, rationalized form.
sec
(
θ
)
=
\sec(\theta)=
sec
(
θ
)
=
______
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cos
(
x
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=
−
0.3
\cos(x) = -0.3
cos
(
x
)
=
−
0.3
. What is
sin
(
9
0
∘
−
x
)
\sin(90^\circ - x)
sin
(
9
0
∘
−
x
)
? ____
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Posted 1 year ago
Question
If
csc
(
θ
)
=
17
8
\csc(\theta) = \frac{17}{8}
csc
(
θ
)
=
8
17
and
0
∘
<
θ
<
9
0
∘
0^\circ < \theta < 90^\circ
0
∘
<
θ
<
9
0
∘
, what is
tan
(
θ
)
\tan(\theta)
tan
(
θ
)
?
\newline
Write your answer in simplified, rationalized form.
\newline
tan
(
θ
)
=
\tan(\theta) =
tan
(
θ
)
=
______
\newline
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Question
Is the sine function even or odd?
\newline
Choices:
\newline
[A]even
\text{[A]even}
[A]even
\newline
[B]odd
\text{[B]odd}
[B]odd
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Question
Write the sentence as an equation.
\newline
89
89
89
is equal to the quotient of
y
y
y
and
17
17
17
\newline
Type a slash (
/
/
/
) if you want to use a division sign.
\newline
_____
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Question
Write the sentence as an equation.
\newline
45
45
45
is equal to the quotient of
z
z
z
and
5
5
5
\newline
Type a slash (
/
/
/
) if you want to use a division sign.
\newline
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Question
Solve for
h
h
h
.
\newline
h
2
+
24
h
=
0
h^2 + 24h = 0
h
2
+
24
h
=
0
\newline
Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.
\newline
h
=
h =
h
=
_____
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Posted 1 year ago
Question
h
2
−
4
h
=
0
h^2 - 4h = 0
h
2
−
4
h
=
0
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Posted 1 year ago
Question
Combine the like terms to create an equivalent expression:
\newline
−
k
−
(
−
8
k
)
=
□
-k-(-8k)=\square
−
k
−
(
−
8
k
)
=
□
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Question
Which of the following degree measures is equal to
5
π
5 \pi
5
π
radians?
\newline
(The number of degrees of arc in a circle is
360
360
360
. The number of radians of arc in a circle is
2
π
2 \pi
2
π
.)
\newline
Choose
1
1
1
answer:
\newline
(A)
14
4
∘
144^{\circ}
14
4
∘
\newline
(B)
90
0
∘
900^{\circ}
90
0
∘
\newline
(C)
1
,
08
0
∘
1,080^{\circ}
1
,
08
0
∘
\newline
(D)
1
,
80
0
∘
1,800^{\circ}
1
,
80
0
∘
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