perplexus.info :: Calculus : Shift in perspective

Shift in perspective (Posted on 2024-01-25)

Find all a such that equation √sinx-√cosx=a has a root.

No Solution Yet Submitted by Danish Ahmed Khan

Rating: 2.0000 (1 votes)

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Not a formal proof but ...

| Comment 1 of 12

Each of √sin(x) and √cos(x) can take on values from 0 to 1.

So the difference can take on values from -1 to 1.

So I assume the answer is the closed interval [-1,1].

Desmos confirmation:

https://www.desmos.com/calculator/ydyojamsoj

Posted by Larry on 2024-01-25 14:17:11

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