1) We know that if [itex]\theta[/itex] is trisectible (with straightedge and compass), then [itex]\theta[/itex]/3 is constructible.(adsbygoogle = window.adsbygoogle || []).push({});

But is it also true that if [itex]\theta[/itex]/3 is constructible, then [itex]\theta[/itex] is trisectible (with straightedge and compass)?

If so, then I can say that since 15^{o}is constructible, we have that 45^{o}is trisectible, right? (because we can copy an angle of 15^{o}three times, thus trisecting the angle 45^{o})

2) Let m,n be integers.

Then m|3n^{3}=> m|n

and n|28n^{3}=> n|m

I spent half an hour thinking about this, but I still have no clue...

Why are the implications (=>) true? Can someone please explain?

3) How can I prove that the acute angle whose cosine is 1/10 is constructible?

I know that if [itex]\theta[/itex] is constructible, then cos[itex]\theta[/itex] is constructible. Butis the converse true?Why or why not?

Any help is appreciated!

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# Homework Help: Trisectible angles | divisibility

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