HONORS TRIGONOMETRY Set 2 - SLIDES 51-55 (featuring tutor Jonathan Park)

sin⁻¹(sin 150°) is not 150°, and your calculator will agree with you right up until the test says otherwise. We open with two practice problems on phase shift and modelling, then work cards 51 through 55 of Honors Trigonometry, filling in the blanks together in real time. You'll learn how to build a Ferris wheel model and why boarding at the bottom forces a negative cosine, which branch inverse cosine and inverse tangent each keep and why they have to choose one, how to evaluate a composition by drawing the right triangle and reading the answer off the sides, why the principal value trap catches students who assume the round trip always returns what they put in, and how to tell whether an SSA triangle has zero, one or two solutions. The two practice problems come first, so you can test phase shift and the Ferris wheel setup before the inverse material starts. ⏱️ CHAPTERS 0:00 Practice — Phase shift of y = 3 sin(2(x − π/4)) 0:36 Practice — Ferris wheel, find the maximum height 1:20 Card 51 — The Ferris Wheel Model (why boarding at the bottom means negative cosine) 2:45 Card 52 — Inverse Cosine and Tangent (the branch each one keeps) 4:08 Card 53 — Compositions by Triangle (draw it, then read it off) 5:27 Card 54 — The Principal Value Trap (sin⁻¹(sin 150°) is not 150°) 6:43 Card 55 — The Ambiguous Case (zero, one or two triangles) 📝 FOLLOW ALONG These are the fill-in-the-blank lecture notes my students use. Print them, pause the video, and write as I write — you'll remember far more than watching passively. 📚 IN THIS SERIES Trigonometry flashcards, one unit at a time: unit circle and identities, graphs and transformations, sum and double angle formulas, solving equations, modelling, and inverse functions. New cards every week. → Full playlist: [ADD PLAYLIST LINK] → Previous: Cards 46–50 (multiple angle equations, transformations, secant and cosecant) [ADD LINK] 💬 Which card gave you the most trouble? Tell me in the comments and I'll cover it in more depth. 🔔 Subscribe if you're taking Honors Trig, Precalculus, or heading into AP Calculus — this series builds straight into it. Seoul Central International School · www.seoulcentral.org #Trigonometry #MathHelp #Precalculus #Math #Maths #SAT #IGCSE