Andrew's Guide to IB Mathematics Universe

Henlo kiddos! Really hope everyone's doing great. Tis is the time of the year when N23s have barely started the course (and I see many of them are doing sequences and series) while M22s better start revising for the exams. Just a friendly reminder: unless you've been told explicitly  by your school that exams won't go forward, please  do yourself a favour and study NOW if you wanna do well. Due to popular demand (~40 votes in the Mocks server, not a small proportion) one of my focuses for this year is writing end-of-topic revision guides. I probably won't write these for EVERY SINGLE TOPIC , as some topics never  show up as a grade 7 question (I'm looking at you, correlation).  For more info re: the structure and the purpose of this booklet, read the second page, but here's a tl;dr: Different target audience - this booklet is aimed at everyone, including those shooting for a 7. Some questions are deliberately  set at that level. For more accessible questions, pl

Hello hello hello! As you know we'll talk about trig equations after trig functions.  After a short hiatus due to me unable to comprehend thermo, I'm now temporarily  back with an ENTIRE (yes, entire) module on trig equations. Have fun with it. Answers included at the end. Link: Where are we going, where have we been? In our journey on trigonometry so far, we started with Pythagorean theorem and right-angled trigonometry. Extending our definition to larger angles, we develop the sine and cosine rules for non-right triangles and then to the entire unit circle.  The "point on the circle" model gives rise to our trigonometric functions, namely, sine and cosine functions. We did a bunch of transformations to fit our function with our data, which is then used to predict future values. The question arises: is there a way we could solve some  equations without using a calculator? Answer: special trig values. More details on that soon. Why are we interested in special trig va