A Levels Trigonometry

In this video, Dr T works through a couple original sample A-Levels trig questions while arguing against the standard in practice which does not allow graphing utilities. Trig functions can be solved using the quadratic formula or factoring, which is not entirely intuitive at first glance. As Dr T remarks several times, the quickest and most reliable method of solving is to use technologies which are here to stay, but for some reason, the British test makers have decided to remain committed to mid-20th century standards at best, allowing only a 1960s style scientific calculator, possibly in a nod to the peak of the British empire, a time after which many Brits decided to stop learning and growing along with the international community. By comparison, American testing agencies allow later-20th century graphing calculators. Aside from cultural commentary, there is strong argument available showing accommodations with technologies help bridge the gap between abstract mathematics and the real world. Nobody at work in 2024 is actually going to do these problems by hand since it’s faster and more reliable to let the technologies do the tedious work - nobody other than A-levels math teachers & test advocates, that is. At any rate, Dr T explains how to use the Pythagorean identity and then quadratic formula to solve for trig values. A main takeaway is that the British methods are slower, and the use of technology is rational, especially considering the relative low-performance among the whole population of students on more rigorous and complicated techniques like those shown in the video. In keeping with the common theme among Dr T’s math videos, he highlights the relationships between algebra, graphs, and table values.