Constructing Inverse Trigonometric Functions
Geometry · Flashcards
GEOMETRY · FLASHCARDS
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QUESTION
Find the restricted interval where
sin
(
x
)
\sin(x)
sin
(
x
)
is decreasing on
[
π
2
,
3
π
2
]
\left[\frac{\pi}{2},\frac{3\pi}{2}\right]
[
2
π
,
2
3
π
]
.
QUESTION
What is the range of
y
=
arctan
(
x
)
y=\arctan(x)
y
=
arctan
(
x
)
?
QUESTION
What monotonic behavior on an interval ensures a function is one-to-one there?
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ANSWER
Always increasing or always decreasing. Monotonic functions are one-to-one since they never repeat outputs.
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