I've been enrolled in a Trigonometry course this semester and I have been enjoying it. I also think the main Pythagorean theorem is one of my new favorite equations, but I just don't understand one thing. Why is the result of the expression equal to one? sin²β + cos²β = 1 We've learned about "proves" where you try to arrive to the answer by choosing the busiest side and in this case the left side, but how would you go about proving this specific this? I heard that more advanced math knowledge was needed (e.g. Calculus) but is that really true or can this be proven using what is learned in Trigonometry itself? Also, in other Trig courses, do instructors actually assign this expression as a homework question all to itself? I thought this was just a formula given to help solve problems and not an actual problem. I also recently learned that Pythagoras was a philosopher and even had his own cult. What are some of the other things this man was known for?