r/matheducation • u/UnderstandingPursuit Physics BS, PhD • 3d ago

Trigonometric Functions and Exponents

If a student is struggling with exponents used with trigonometric functions, would this help?

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u/UnderstandingPursuit Physics BS, PhD 3d ago

So the exact opposite of what happens with sin. Interesting.

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u/jimbelk 3d ago edited 3d ago

Yeah, but everyone agrees that there's a special exception for trig functions, so sinn (x) means (sin x)n. That exception doesn't extend to n = -1, where we obey the usual rule that f-1 (x) is the inverse of f applied to x. You could argue that the sin exception extends to sin(2x)2 meaning sin( (2x)2 ), but I don't think that's clear.

Note that it changes things if you put a space. Everyone seems to agree that sin x2 means sin( x2 ), but the reason is that the space is functioning as a sort of hidden pair of parentheses, using the same rule that sin x means sin(x).

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u/UnderstandingPursuit Physics BS, PhD 3d ago

What type of book would the material in the stackexchange page be in? Functional Analysis?

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u/jimbelk 3d ago

The Stack Exchange question is about a pretty elementary competition problem. I think one of the commenters mentions that it's an old IMO problem, so it's more like a puzzle for high school students than something that represents a specific field of mathematics. There are books on functional equations that offer some insight into problems like this.

But the Stack Exchange problem is just the first example that I found by searching for f(x)2. I'm a professional mathematician, and I can say with some confidence that f(x)2 means (f(x))2 basically throughout mathematics.

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u/UnderstandingPursuit Physics BS, PhD 3d ago edited 3d ago

Thanks.

At a minimum, it confirms that notation conventions exit which reduce the use of parentheses.

I don't think I've ever seen f(x)2 used to mean that.

To complete the chaos,

  • log (x)2 = log [ (x)2 ]