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Compound angles proof 
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#1
Jan314, 09:45 AM

P: 271

Hello,
simple question. My textbook (Bostock and Chandler  Pure Mathematics 1) says something that really surprises me. It goes on to say; Thanks! 


#2
Jan314, 02:16 PM

Sci Advisor
P: 6,066

It is trivially obvious, why are you puzzled? What is contradictory? I presume the statement is for k a positive integer.



#3
Jan314, 02:54 PM

P: 271

It is not explicitly stated in my textbook what is meant by k, but all related questions deal with positive numbers, fractions and integers. 


#4
Jan414, 05:51 PM

Sci Advisor
P: 6,066

Compound angles proof
kθ = 2π, therefore θ =2π/k. As long as k is an integer, what else is needed?



#5
Jan414, 06:20 PM

P: 16

Perhaps you're taking the context of the bolded statement to be total human mathematical development, rather than the mathematical development up to that point in the text?



#6
Jan514, 01:24 AM

P: 93

I agree with Integrand. It sounds like the textbook authors want to make it clear that they are not providing a proof. They are distinguishing a conjecture making moment. If the text takes an investigation approach, then it probably encourages readers to do similar activities to develop conjectures and then better proofs.
The part that you say is contradictory is what I would call Proof by Authority. These are moments in textbooks where the author just asks the reader to accept the math without other justifications. This is often necessary because a proof requires advanced mathematics or may take too long. There's a lot of this in algebra texts: fractional exponents, calculating determinants, formulae of SA and volume of spheres. Typically the reader is just given these rules. 


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