✓ Верните мой 2007-й год | Всероссийская олимпиада. Финал-2009 | Ботай со мной #157 | Борис Трушин

How many times does the function f(x) = cos x · cos(x/2) · cos(x/3) · … · cos(x/2009) change sign on the interval [0; 2009π/2] ? How to support the channel: Bitcoin: bc1qwzx9t9mz5h5q8sgtz74mdgedxd5wu0g9kq6q5m Ethereum: 0xAE872DcA8B135cf62Df4B36bE576a2EE64c6066a USDT (ERC20): 0xAE872DcA8B135cf62Df4B36bE576a2EE64c6066a Regular help (Boosty): https://boosty.to/trushinbv Regular help (YouTube): https://www.youtube.com/trushinbv/join Regular help (Patreon):   / trushinbv   Regular help (Sponsr): https://sponsr.ru/trushinbv One-time assistance (Yu-money, former Yandex.Money): https://yoomoney.ru/to/410011017613074 One-time assistance (PayPal): https://paypal.me/boristrushin One-time assistance (Donation Alerts): https://www.donationalerts.com/r/bori... One-time assistance (Sber): 2202 2001 0398 5451 This academic year I am teaching three courses: ✔ "Preparation for the Unified State Exam in specialized mathematics from 0 to 70 points (10-11 grades)": https://trushinbv.ru/ege70 It is suitable for both tenth-graders who want to consistently solve 70+ exams a year before the Unified State Exam, and for eleventh-graders who know almost nothing, but want to pass the exam in a year for decent scores. During the course, we will master both the entire test section and many tasks from the difficult part of the Unified State Exam. ✔ "Preparation for the Unified State Exam in specialized mathematics from 60 to 100 points (11th grade)": https://trushinbv.ru/ege100 For those who already know mathematics at a basic level and want to master it to 90+ in a year. There, we will mainly learn to solve tasks from the difficult part of the Unified State Exam, but we will also delve a little into some meaningful tasks from the test section. (If an eleventh-grader has sufficient motivation, they can study simultaneously on both of these courses - http://trushinbv.ru/egepack - their programs are coordinated with each other) ✔ "Preparation for the list of Olympiads in Mathematics (10-11 grades)": https://trushinbv.ru/olymp First of all, this course is for eleventh-graders who have mastered the standard school curriculum at least with a "four", and want to prepare for Olympiads such as Phystech, Lomonosov, OMMO and PVG in six months, in order to try to get a diploma in at least one of them. In addition, my last year's courses are available in recording: ✔ "Preparation for the OGE": https://trushinbv.ru/oge9 This is a recording of a large annual course that I conducted a couple of years ago. This year I will not have new courses for the 9th grade. ✔ Mini-courses on individual Unified State Exam tasks: Probability Theory from scratch to the Unified State Exam (Tasks 4 and 5): https://trushinbv.ru/egeTV Equations and Inequalities (Tasks 13 and 15): https://trushinbv.ru/egeAL Stereometry (Task 14): https://trushinbv.ru/egeST Economic Problems (Task 16): https://trushinbv.ru/egeEC Planimetry (Task 17): https://trushinbv.ru/egePL Problems with a Parameter (Task 18): https://trushinbv.ru/egePR Number Theory (Task 19): https://trushinbv.ru/egeTC ✔ Mini-courses on listed Olympiads: Phystech Olympiad: https://trushinbv.ru/fizteh OMMO Olympiad: https://trushinbv.ru/ommo Lomonosov and PVG Olympiad: https://trushinbv.ru/lomonosov Other Foxford courses: https://trushinbv.ru/courses Foxford tutors: https://trushinbv.ru/coach Book "Combinatorics: from zero to Olympiads": https://trushinbv.ru/kombinatorika Book "Number Theory: from zero to Euler's theorem": https://trushinbv.ru/teoriiachisel Merchant store: https://trushinbv.ru/shop Channel guide: https://trushinbv.ru/book VKontakte: https://vk.com/ege_trushin TikTok:   / trushinbv   Twitter:   / trushinbv   Instagram:   / trushinbv   Telegram: https://t.me/trushinbv Facebook:   / trushinbv   YouTube:    / trushinbv   Personal website: https://TrushinBV.ru