In problems
1
−
6
,
state the domain and range of each function.
y
=
sin
−
1
x
Expert Solution & Answer
To determine
The domain and range of function y=sin−1x.
Answer to Problem 1RE
Solution:
The domain of the function y=sin−1x is [−1,1] and its range is [−π2,π2].
Explanation of Solution
Given information:
y=sin−1x.
Explanation:
Let a function y=sin−1x⇒x=siny.
As, the domain of the function x=siny is −∞<y<∞ and its range is −1≤x≤1.
If, the domain of x=siny is restricted to the interval [−π2,π2], then the restricted function x=siny;−π2≤y≤π2 is one-one and has an inverse function.
Thus, y=sin−1x is an inverse of a function x=siny.
Now, the restricted sine function x=siny receives as input an angle or real number in the interval [−π2,π2] and output a real number in the interval [−1,1].
Therefore, the inverse sine function y=sin−1x receives as input a real number x in the interval [−1,1], its domain and output an angle or real number in the interval [−π2,π2], its range.
Hence, the domain of the function y=sin−1x is [−1,1] and its range is [−π2,π2].
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Express the following function as a purely algebraic function.
Answer
sin (cos-¹ (²-))
sin (cos-¹(²)) =
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Suppose that the height above ground of a person sitting on a Ferris wheel is described by the following functionh(t) = 18.4 + 16.3 sin (2pie/5 t)In this function, ℎ(t) is the height above ground (in meters) and t is the time (in minutes). The ride begins at t = 0 minutes.
Find the period of the function and interpret its meaning in the context of this problem in complete sentence(s).b) Find the maximum and minimum values and interpret its meaning in the context of this problem in complete sentence(s). Do not round. c) During the first 10 minutes, when will the person be 25 meters above the ground? Round all answers to the nearest hundredth. Note: The graphing calculator may be used to solve part c).
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