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Let’s check out your problem:
sin
−
1
(
−
1
)
\sin ^{-1}(-1)
sin
−
1
(
−
1
)
=
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Math Problems
Algebra 1
Evaluate integers raised to rational exponents
Full solution
Q.
sin
−
1
(
−
1
)
\sin ^{-1}(-1)
sin
−
1
(
−
1
)
=
Question Prompt:
Question prompt: What is the value of
sin
−
1
(
−
1
)
\sin^{-1}(-1)
sin
−
1
(
−
1
)
?
Understand the Problem:
Understand the problem.
\newline
We need to find the angle whose sine is
−
1
-1
−
1
.
Recall Definition:
Recall the definition of the inverse sine function. The inverse sine function,
sin
−
1
(
x
)
\sin^{-1}(x)
sin
−
1
(
x
)
, gives us the angle whose sine is
x
x
x
.
Recall Range:
Recall the range of the inverse sine function.
\newline
The range of
sin
−
1
(
x
)
\sin^{-1}(x)
sin
−
1
(
x
)
is from
−
π
2
-\frac{\pi}{2}
−
2
π
to
π
2
\frac{\pi}{2}
2
π
.
Identify Angle:
Identify the angle within the range of the inverse sine function whose sine is
−
1
-1
−
1
.
\newline
The sine of
−
π
/
2
-\pi/2
−
π
/2
is
−
1
-1
−
1
.
Write Final Answer:
Write the final answer.
sin
−
1
(
−
1
)
=
−
π
2
\sin^{-1}(-1) = -\frac{\pi}{2}
sin
−
1
(
−
1
)
=
−
2
π
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\newline
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Write your answer in the form
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\newline
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\newline
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