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Chapter 4: Problem 93

Use a graphing utility to graph the function. $$f(x)=\pi-\sin ^{-1}\left(\frac{2}{3}\right)$$

Short Answer

Expert verified
The function \( f(x) = \pi - \sin^{-1}\left(\frac{2}{3}\right) \) is a constant function, and its graph is a straight horizontal line on the y-axis at the constant value obtained which is approximately 2.51.

Step by step solution

01

Determine the value of \(\sin^{-1}\left(\frac{2}{3}\right)\)

The sine inverse of any number is defined as the angle whose sine is that number. Since sine of an angle is opposite/hypotenuse, we know that our angle will be between -蟺/2 and 蟺/2 (or between -90 and 90 degrees) as sine is defined in these angles. Since we do not have any given angle and are to solve it over a calculator, we can just plug the value in the calculator to get the value of \(\sin^{-1}\left(\frac{2}{3}\right)\).
02

Subtract \(\sin^{-1}\left(\frac{2}{3}\right)\) from 蟺

Now that we know the value of \(\sin^{-1}\left(\frac{2}{3}\right)\), we will subtract this value from 蟺. Let's use a calculator to perform this calculation. 蟺 is constant and equals approximately 3.1416.
03

Plot the function

Since the function \( f(x) = \pi - \sin^{-1}\left(\frac{2}{3}\right) \) is a constant function, it is a straight horizontal line on the graph at the calculated constant value.

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Most popular questions from this chapter

Sketch a graph of the function and compare the graph of \(g\) with the graph of \(f(x)=\arcsin x\). $$g(x)=\arcsin \frac{x}{2}$$

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