This circuit has it all for your students to review their trigonometry! 48 total questions (only 8 require the use of a calculator, and assuming the students are doing it correctly, the 8 questions all come in a row in the middle of the circuit). The circuit starts with ideas from geometry (Pythagorean triples, special right triangles), and moves into Law of Sines / Cosines / area formulas and other formulas involving radians. There are problems which require using the unit circle and solving equations, identifying features of graphs of sinusoids and simplifying trig expressions, all the way to double angle identities and more! Perfect for Test Prep / ACT review.
Students begin on the first problem and then search for their answer to advance in the circuit -- my classroom hums when students are working in this format. They lean over effortlessly and help each other, they talk about math, and they don't get up when the bell rings!
My colleagues and I check our circuits very carefully but should you ever get stuck or find an error, please contact me!
Here's what I wrote in an email to a colleague as we were editing this circuit:
"The circuit does start with geometry. But when I taught precal I found that most of my students either never learned the trig the way they should have in geometry or they had forgotten it. It is so important for building the foundation for the rest of trig! So I would reteach it. It helped their ACT scores anyway.
"I remember when I was a student in honors algebra two (I have weird math memories) we vaulted straight in to sin(theta) = y/r and I had not been in honors geometry the year before so I was so lost. So when I teach it I always spend at least a week on right triangle trig and then at least week on word problems / law of sines / law of cosines / formulas / conversions/ etc and then time sketching angles and reference angles and triangles in the x-y plane and THEN go into the unit circle. Then they know where it's coming from.
"I think the path of the circuit lays out how I would teach the trig. There's no polar or parametric (really) on the circuit because a bunch of regular kids probably wouldn't get that far anyway and that stuff isn't as important in AB calculus or on the ACT. But, my students who end up getting wildlife management degrees (or similar) from Mississippi state say the trig they learned was so important!"
And there you have it! I have some other trig circuits... the using the unit circle one and right triangle trig (both no calculator) are two of my favorites. I have a Law of Cosines/Sines one and also some ones that get at simplifying / solving trig equations.