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Let’s check out your problem:
θ
\theta
θ
is an
acute angle
. Find the value of
θ
\theta
θ
in degrees.
\newline
sec
(
θ
)
=
2
\sec(\theta) = \sqrt{2}
sec
(
θ
)
=
2
\newline
θ
=
\theta =
θ
=
____
°
\degree
°
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Math Problems
Algebra 2
Inverses of csc, sec, and cot
Full solution
Q.
θ
\theta
θ
is an acute angle. Find the value of
θ
\theta
θ
in degrees.
\newline
sec
(
θ
)
=
2
\sec(\theta) = \sqrt{2}
sec
(
θ
)
=
2
\newline
θ
=
\theta =
θ
=
____
°
\degree
°
Secant and Cosine Relationship:
sec
(
θ
)
\sec(\theta)
sec
(
θ
)
is the reciprocal of
cos
(
θ
)
\cos(\theta)
cos
(
θ
)
, so if
sec
(
θ
)
=
2
\sec(\theta) = \sqrt{2}
sec
(
θ
)
=
2
, then
cos
(
θ
)
=
1
2
\cos(\theta) = \frac{1}{\sqrt{2}}
cos
(
θ
)
=
2
1
.
Secant Value Calculation:
But wait, we know that
cos
(
45
°
)
=
2
/
2
\cos(45°) = \sqrt{2}/2
cos
(
45°
)
=
2
/2
, which is the same as
1
/
2
1/\sqrt{2}
1/
2
if we rationalize the denominator.
More problems from Inverses of csc, sec, and cot
Question
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
∘
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Posted 1 year ago
Question
Kimi's school is
15
15
15
kilometers west of her house and
8
8
8
kilometers south of her friend Franklin's house. Every day, Kimi bicycles from her house to her school. After school, she bicycles from her school to Franklin's house. Before dinner, she bicycles home on a bike path that goes straight from Franklin's house to her own house. How far does Kimi bicycle each day?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
kilometers
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Posted 1 year ago
Question
Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth.
\newline
cos
3
5
∘
=
\cos 35^\circ =
cos
3
5
∘
=
__
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Posted 1 year ago
Question
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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Posted 1 year ago
Question
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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Posted 1 year ago
Question
The terminal side of an angle
θ
\theta
θ
in standard position intersects the unit circle at
(
84
85
,
13
85
)
(\frac{84}{85}, \frac{13}{85})
(
85
84
,
85
13
)
. What is
cos
(
θ
)
\cos(\theta)
cos
(
θ
)
?
\newline
Write your answer in simplified, rationalized form.
\newline
______
Get tutor help
Posted 1 year ago
Question
−
9
0
∘
<
θ
<
9
0
∘
-90^\circ < \theta < 90^\circ
−
9
0
∘
<
θ
<
9
0
∘
. Find the value of
θ
\theta
θ
in degrees.
\newline
tan
(
θ
)
=
0
\tan(\theta) = 0
tan
(
θ
)
=
0
\newline
Write your answer in simplified, rationalized form. Do not round.
\newline
θ
=
\theta =
θ
=
____
∘
^\circ
∘
\newline
Get tutor help
Posted 1 year ago
Question
Evaluate. Write your answer in simplified, rationalized form. Do not round.
\newline
csc
6
0
∘
=
\csc 60^\circ =
csc
6
0
∘
=
______
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Posted 1 year ago
Question
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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Posted 1 year ago
Question
You pick a card at random, put it back, and then pick another card at random.
\newline
4
4
4
\newline
5
5
5
\newline
6
6
6
\newline
7
7
7
\newline
What is the probability of picking a number greater than
5
5
5
and then picking a
4
4
4
?
\newline
Write your answer as a percentage.
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Posted 5 months ago
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