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#### xyz_1965

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- Jul 26, 2020

- 81

Why does arcsin (sin x) = x?

Can it be that trig functions and their inverse undo each other?

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- Jul 26, 2020

- 81

Why does arcsin (sin x) = x?

Can it be that trig functions and their inverse undo each other?

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- Jul 26, 2020

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What? Can you explain further? Why is the answer pi/6?You have to be mindful of the one-to-one interval over which the inverse function is defined. For example:

\(\displaystyle \arcsin\left(\sin\left(\frac{5\pi}{6}\right)\right)=\frac{\pi}{6}\)

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What domain do we use for the sine function such that we can define an inverse?What? Can you explain further? Why is the answer pi/6?

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- Jul 26, 2020

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Domain: [-1, 1].What domain do we use for the sine function such that we can define an inverse?

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- Jul 26, 2020

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[-pi/2, pi/2]No, that's the range.

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Yes...is \(\displaystyle \frac{5\pi}{6}\) in that domain?[-pi/2, pi/2]

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- Jul 26, 2020

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Yes, it is.Yes...is \(\displaystyle \frac{5\pi}{6}\) in that domain?

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No, it is outside that since:Yes, it is.

5/6 > 1/2

What is \(\displaystyle \sin\left(\frac{5\pi}{6}\right)\) ?

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- Jul 26, 2020

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I just got home. Let me see: sin(5pi/6) = 1/2.No, it is outside that since:

5/6 > 1/2

What is \(\displaystyle \sin\left(\frac{5\pi}{6}\right)\) ?

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Yes. Now what angle within the restricted domain returns that same value from the sine function?I just got home. Let me see: sin(5pi/6) = 1/2.

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- Jul 26, 2020

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Using the unit circle, I found the angle to be pi/6.Yes. Now what angle within the restricted domain returns that same value from the sine function?

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Good, the puzzle is thus completed.Using the unit circle, I found the angle to be pi/6.

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- Jul 26, 2020

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Wasted too much time solving this puzzle. If I do this for every problem, I'll never get to calculus 1.Good, the puzzle is thus completed.

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- Jul 26, 2020

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I gotta speed up this precalculus trek. It is on hold as I wait for my Michael Sullivan 5th Edition Precalculus textbook to arrive.If you now understand how this works I'd say it was time well spent.