1. The problem statement, all variables and given/known data Be x an element in the interval [Pi/4, 3Pi/4] express cos(2x), sin x, sin (x+pi) in terms of x. You must know that, for this question, cos x = z and z will always be < 0. 2. Relevant equations cos(2x) = 2 (cos(x))^2 - 1 cos(2x) = cos^2 x - sin ^2 x sin^2 x + cos ^2 x = 1 sin(x+pi) = -sin x 3. The attempt at a solution I'm doing this for a friend, and it's been ages since I have tried this type of problem. Anyways, for cos(2x) I just used the identity cos(2x) = cos^2 x - sen ^2 x which can be proven with the Pythagorean theorem to be actually another form of cos(2x) = 2 cos^2 x - 1. I don't know, though, if that would be the final answer of if I need to express it further (since basically I have everything expressed as constants and cos), making what I think is the answer 2z^2 - 1. I have really no idea for the sin(x), but I guess I will be using the Pythagorean identity. I got this document like 5 minutes ago and I've got to leave, so yeah. Just skimmed it and nothing came to mind. The real problem is, though, sin(x+pi). If sin(x+pi) = -sin x using the sum of angles formula (and everything with a cosine cancels in there) how can I express sen(x+pi) in terms of the cosine? Thanks for the help.