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Problem 73 Hard Difficulty

Graph the given functions on the same screen. How are these graphs related?

$ y = \sin x $ , $ \frac{-\pi}{2} \le x \le \frac{\pi}{2} $ ; $ \sin^{-1} x $ ; $ y = x $

Answer

The graph of $\sin ^{-1} x$ is the reflection of the graph of
$\sin x$ about the line $y=x$.

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Video Transcript

for this problem. We're using a graphing calculator. We're going to graft the sine function and the inverse sign function and the line Y equals X. So we go into the y equals menu when we type like will sign of X. And then for the 2nd 1 we do Enver sign of X and then for the 3rd 1 we do y equals X. Now let's make sure we're in radiant mode. So go to mode. And if your calculators not currently in radiance change into radiance Okay, now let's go to window and we can set our window dimensions. We want X values to go from negative pi over to two pi over two so we can change those. We can actually use the pie button. So negative pie divided by two two pi divided by two. Okay, for the y values. Perhaps we go from negative to to to We can always change that if we want to do something different. So let's take a look at our graph. Okay, President Trace will help us see what's what. So the blue one is the sign graph just the part of the sign graph that goes between negative pi over two and pi over two. The red one is the inverse sign graph, and the black one is the line y equals X. So what we noticed is that sign and Enver sign our reflections across the line Y equals X.

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