The discussion centers on understanding trigonometric equations and identities, particularly the equation tan²(2x) = 3. Participants emphasize the importance of the unit circle and the foundational identity cos²(x) + sin²(x) = 1 in solving trigonometric problems. A key takeaway is the method of substituting variables, such as letting θ = 2x, to simplify the equation before solving. The conversation highlights the necessity of recognizing patterns in trigonometric identities to effectively tackle complex equations.
PREREQUISITESStudents struggling with trigonometry, educators seeking to clarify concepts, and anyone looking to strengthen their understanding of trigonometric identities and equations.
@Tyrion101, no, they are not the only solutions, in fact these aren't even solutions of the original equation, which was ##tan^2(2x) = 3##. Unless there is a restricted domain, which you didn't mention, there are an infinite number of solutions.Tyrion101 said:I think I understand, so the number of answers varies depending on what function you are using, and I may not understand all of the functions well, however with your info I have figured out that pi/3, and 5pi/3 are the only solutions