Trigonometry Tutorial Weekly

So you want to learn trigonometry properly

Most people try to memorize SOHCAHTOA and then struggle through a bunch of word problems that don't really teach them anything. I found Trigonometry Tutorial Weekly a few years ago when I was putting together study material for some students. The format is straightforward — weekly lessons broken into concept modules, practice sets, and occasional real-world application breakdowns. You can find it at trigweekly dot com.

What makes it stand out isn't any single lesson. It's the pacing. They don't throw radians at you on day one. They start with ratios, build the unit circle slowly, and only later introduce identities. I went through the first three modules myself to see if the explanations were solid enough to recommend, and they held up. Download the weekly PDF and work through it in order. Don't skip ahead. The first time I tried that, I spent two weeks confused about why my angle conversions kept coming out wrong because nobody had properly explained the relationship between degree measure and arc length by that point. The material assumes you've completed the previous week's work. It's not a reference document. It's a curriculum. The practice sets are the part most people gloss over. Each module comes with about twelve problems of varying difficulty. Do all of them before moving on. The harder ones — usually problems four through six in each set — are where the actual understanding happens. I've seen too many students breeze through the first three and then get stuck on problem five because they never actually internalized what a coterminal angle does to a function's output.

There's a companion problem bank if you need extra work, and I'd recommend using it once you finish a module and still feel shaky. The explanations are detailed enough that you can self-study without a textbook. But you do need a graphing calculator or Desmos. I learned that the hard way.

A specific problem I ran into

During the polar coordinates module, I hit a section on converting between rectangular and polar forms of conic sections. The tutorial explains the conversion formulas correctly, but the example it uses — a spiral intersecting a circle — has a subtle edge case that isn't mentioned. When the spiral equation involves a tangent function, you get undefined points at odd multiples of pi over two. The tutorial shows the conversion and then immediately gives the solution without addressing that those undefined points still exist in the polar graph. I caught it because I was plugging the converted equation into Desmos and the graph was breaking at exactly those angles. The workaround was to manually exclude those values when plotting. If you're doing this by hand, just note the asymptotes separately and redraw those sections. It's a small thing, but it's the kind of gap that trips people up on exams. The rest of the tutorial is solid, but no single resource is going to cover every edge case.

Things beginners miss

One thing that trips almost everyone up is the difference between solving for an angle and solving for a side length in a triangle. The law of sines and the law of cosines use completely different approaches depending on which you're given. A lot of students try to force one formula to do the work of both. The tutorial covers this in week seven, but only if you've been keeping up with the identity derivations from earlier weeks. If you haven't, you'll be guessing at which formula to reach for instead of knowing why one works and the other doesn't. Another common pitfall: inverse trig functions. People treat arcsin, arccos, and arctan like they just "undo" the regular functions. They do, sort of — but only within restricted domains. The tutorial puts this in week ten, and it's the week where I see the most complaints. The restriction on arcsin is negative pi over two to positive pi over two. If a problem asks for an angle outside that range that still satisfies the sine value, you need to use the unit circle symmetry, not just punch it into a calculator. That part is worth re-reading twice.

What this resource doesn't do well

The tutorial is strong on classical trig — right triangles, the unit circle, identities, inverse functions, and basic polar coordinates. It gets weaker on applications involving vectors or complex numbers. If you're taking a pre-calculus or calculus course that includes those topics, you'll need supplementary material. The weekly cadence also means you're locked into their pace. If you fall behind, the gaps compound quickly because each week builds directly on the previous one. The price is reasonable for what it is, but some of the older modules haven't been updated to match modern calculator notation. A couple of the answer keys reference scientific calculator button sequences that aren't standard on the TI-84 or similar devices. I've checked the errata page and they have a small update for that, but it's spread across three different announcements. If you're working through it, bookmark the announcements section and check it after every module. If you want something faster or more visual, Khan Academy covers similar ground with video walkthroughs. But if you prefer working through written explanations at your own speed and want practice problems that match the lesson rather than randomly generated ones, this is one of the better free resources available. Just don't treat it like a shortcut. It works, but only if you actually do the work each week.