We’ve done some special right triangle practice in the first quarter, but when you remove the context of the application (it was converting rectangular complex numbers to polar form) the students struggle. I don’t want them just memorizing or using some finger trick to get these trig ratios, I want them having some idea on how they can be derived. Many of them “knew” this stuff when they did it last year in Algebra II. but I tested their carried over knowledge by giving an 8 question quiz on sine, cosine, and tangent of different radian values and 8 minutes. The median score for this pretest was 0/8. But after discussing some strategies for finding the values, the median score for the post test at the end of the block was 7/8, and the median score for a similar quiz at the beginning of the next block (no homework on this stuff was assigned) was 8/8. They’re much more confident at solving these type of questions and most of them don’t need the entire 8 minutes, I’d bet most are done in half that time. I don’t love the idea of having to practice speed, but I really only care that they’re fast enough at finding these values. If they can “jump” that high, then I don’t care if they can “jump” higher. This all sort of fits in with Michael Pershan’s most recent fantastic post, found here. These students need to be somewhat proficient at calculating these exact values without a calculator because all their future standardized tests (SAT, ACT, AP, or IB) will have some sort of non-calculator portion, let alone the goal for deeper understanding. Where their knowledge fits in with the deriving the answer vs memorizing the answer vs at what step did they memorize the answer,… I don’t know. Here’s my key for the second quiz. Although I’ve been teaching math for more than a decade, I do NOT have these values memorized. I use my memorized facts (the two triangles, SOHCAHTOA, and the quadrants) to calculate the values if I need them.