Recent content by tonit

yeah, I'll keep that in my mind :smile:

alright so after simplifying I get 16sin^4\theta - 12sin^2\theta + 1 = 0 now it's pretty obvious to solve. thanks :D

I guess the first one would be easier, and I got 16sin^5\theta - 20sin^3\theta + 5sin\theta = 1 I'm stuck again...:@

I got sin^5θ - 10sin^3θ cos^2θ + 5sinθ cos^4θ = 1 and i5sin^4θcosθ - i10sin^2θcos^3θ + icos^5θ = 0 where θ = \frac{\pi}{10} = 18^{\circ} is this ok?

e^{i\frac{2\pi }{5}} = sin(18) + icos18 right?

Homework Statement Find 5th roots of unity solving algebraically x^5-1=0. Using the result, find sin18 and cos18The Attempt at a Solution x^5 = 1\\ x = \sqrt[5]{1} since we have 5 roots: x_k, k = 0,1,2,3,4 \\ \\ x_k = e^{i\frac{2k\pi}{n}}, n=5 \\ x_0 = e^{i0} = 1\\ x_1 =...

Thank you HallsofIvy. It's all clear now :D

ok. Thank you!...very helpful

Homework Statement Let's say I want to find the inverse of \bar{4} in \mathbb{Z}_{13}. So I get 13 = 4\cdot 3 + 1 and so 1 = 13 - 4\cdot 3. But this doesn't show that 3 is inverse of 4. So I have to express 4 = 3\cdot 1 + 1 which yields that 1 = 4 - 1\cdot 3 = 4 - 3\cdot (13 - 3\cdot 4) =...

Direct product of two groups G and H, is the group G\times H = \{ (g,h) | g \in G, h \in H \}. If * is the operation of G and H, (g,h)*(g_1,h_1) = (g*g_1,h*h_1). Similarly the inverse (g,h)^{-1} = (g^{-1},h^{-1}). Now can you find any element (g,h) \in \mathbb{Z}_6\times \mathbb{Z}_3 such that...

If H and K are subgroups of G, suppose H⊆K. So we have that |H| divides |K|, and they both divide |G|. If it would happen that |G| = p^ka^r where p, a are different primes, then G would have two subgroups M and N such that |M| divides p, |N| divides a, M ⊄ N and N ⊄ M, thus contradicting the...

Reflexive doesn't mean a = a. The equality is a relation of equivalence, but a relation of equivalence need not be "=".

Homework Statement Show that the following conditions are equivalent for a finite group G: 1.G is cyclic and |G| = p^n where p is prime and n\geq 0 2.If H and K are subgroups of G, either H⊆K or K⊆H. The Attempt at a Solution 1 => 2. Let H,K be subgroups of G = <g> where o(g)...

Well, you should try to work with classes. As there is no way the program does it automatically for you. You should learn some OOP, and it will make your life easier when you work with C++. That's how program's work. They call functions. For example, each time you post something on the forum...

yeah. Thanks for the help, I'm learning a lot at this forum really :D