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# Trig Substitution watch

1. http://mathshelper.co.uk/STEP%20II%201989.pdf

I was doing the first question on that paper and I got upto solving cos(3x) = sqrt(3)/2 which has infinite solutions. My question is how do I know which 3 solutions would actually work in the original polynomial since the trig substitution gives infinite solutions.
2. (Original post by tsrguru)
http://mathshelper.co.uk/STEP%20II%201989.pdf

I was doing the first question on that paper and I got upto solving cos(3x) = sqrt(3)/2 which has infinite solutions. My question is how do I know which 3 solutions would actually work in the original polynomial since the trig substitution gives infinite solutions.
I haven't worked the question but I would have thought that you would take the principle values of theta (i.e. in the range which give distinct values of as it's only the values of that you're actually looking for to be distinct, not . Hope that makes sense?

EDIT: What I've written above is probably not too clear . Basically, there are an infinite number of solutions for theta, but only 3 distinct solutions for arise from those, you just need to identify which ones lead to distinct values of .
3. Your solutions are going to be based on the values of cos x when cos(3x) = sqrt(3/2).

Although there are an infinite number of solutions to cos(3x)=sqrt(3/2), these will only give 3 different values for cos(x).
4. (Original post by DFranklin)
Your solutions are going to be based on the values of cos x when cos(3x) = sqrt(3/2).

Although there are an infinite number of solutions to cos(3x)=sqrt(3/2), these will only give 3 different values for cos(x).
Thanks! that clarifies everything.

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