Constructing Inverse Trigonometric Functions
Geometry · Flashcards · Application
GEOMETRY · FLASHCARDS
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QUESTION
Identify whether
sin
(
x
)
\sin(x)
sin
(
x
)
is one-to-one on
[
0
,
2
π
]
\left[0,2\pi\right]
[
0
,
2
π
]
.
QUESTION
Evaluate
tan
(
arctan
(
x
)
)
\tan\left(\arctan(x)\right)
tan
(
arctan
(
x
)
)
for
x
∈
(
−
∞
,
∞
)
x\in\left(-\infty,\infty\right)
x
∈
(
−
∞
,
∞
)
.
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
]
.
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ANSWER
[
π
2
,
3
π
2
]
\left[\frac{\pi}{2},\frac{3\pi}{2}\right]
[
2
π
,
2
3
π
]
. The sine function is decreasing throughout this entire interval.
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