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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In a certain piston engine, the distance x (in centimeters) from the center of the drive shaft to head of piston is given by the function
(Function is in the image provided)
Where (theta) is an angle in degrees between the crank and the path of the piston head. Find x when (theta) = 30(degrees) and when (theta) = 45(degrees) round answer to the nearest thousandth centimeter.
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