MAT 172 — Pre-Calculus Trigonometry
14 tools
MAT 172
Unit Circle
All 16 standard angles with exact sine, cosine, and tangent values. Hover any point to explore coordinates and trig values.
MAT 172
Sine & Cosine Waves
Drag sliders to reshape amplitude, period, phase shift and vertical shift in real time. Animated trace dots show exactly where each function is.
MAT 172
Reference Angles
Visual guide to finding reference angles in all four quadrants, ASTC sign rules, and an interactive angle diagram with instant feedback.
MAT 172
Trig Identities
Pythagorean, reciprocal, quotient, and co-function identities — all visualized, with a live proof that sin²θ + cos²θ = 1 at every angle.
MAT 172
Inverse Trig Functions
arcsin, arccos, arctan — working backwards from ratio to angle. Domain restrictions, evaluation, compositions, and interactive unit circle.
MAT 172
Solving Trig Equations with Identities
Section 7.1 — use identities to get one trig function, isolate it, find all solutions using reference angles and ASTC.
MAT 172
Sum & Difference Identities
Section 7.2 — exact values for non-special angles by splitting into 30°, 45°, 60°. All six formulas with worked examples and interactive verifier.
MAT 172
Unit Circle → Wave
Live animation: watch a point spin around the unit circle while its height draws the sine wave in real time. Switch between sin, cos, and both together.
MAT 172
The Tangent Function
The odd one out — no amplitude, asymptotes at every π/2 + nπ, period π not 2π. Interactive graph explorer, key values table, and practice problems.
MAT 172
Product-to-Sum & Sum-to-Product
Section 7.4 — all 7 formulas with worked examples from class notes and an interactive verifier for all formula modes.
MAT 172
Solving Trig Equations (7.5)
Section 7.5 — all 5 methods: linear, square root, quadratic, multiple angles, and calculator. Interactive unit circle solver included.
MAT 172
Conic Sections
All four conics — circles, parabolas, ellipses, hyperbolas. Live interactive graphs, standard form equations, worked examples, and exam reminders for each.
MAT 172
Parametric Equations
Sections 8.6–8.7 — x and y as functions of t. Live animation, eliminating the parameter, curve shapes, projectile motion simulator, and curve explorer.
Coming soon
Graphing Transformations
How shifting, stretching, and reflecting changes trig graphs — amplitude, period, phase shift.
MAT 172
Law of Sines & Cosines
Sections 8.1–8.2 — solving oblique triangles. Decision flowchart, ambiguous case, Heron's formula, and interactive triangle solvers.
The Lab — where it gets real
8 tools
The Lab
Blogarithmic Functions
Where MAT 172 meets the real world — pH, log reductions, serial dilutions, decibels, Richter scale, and an interactive log grapher.
The Lab
Homogenizer & Pressure Waves
PSI on your homogenizer is a sine wave. Adjust pressure and flow rate to see how cavitation breaks fat globules — the unit circle in your dairy pipe.
The Lab
The Bloop
A sine wave from the bottom of the world. How a 1997 mystery sound connects the unit circle, ocean acoustics, and your homogenizer PSI.
The Lab
Centrifugal Force
Why your centrifuge is just a unit circle. F = mω²r decoded — the butterfat test, RPM to radians, and the trig running your QA protocol since 1890.
The Lab
Microbial Growth Curves
Lag, log, stationary, death — the math of how bacteria grow, why log phase is exponential, and what slow acidification looks like on a curve.
The Lab
Food Safety Math
D-values, Z-values, thermal death time — the logarithms running your pasteurization system. The PMO numbers aren't arbitrary. They're math.
The Lab
Science of the Octagon
The same math behind a centrifuge spin and a spinning kick. Angular velocity, vector strikes, energy systems, and momentum — with the lactate-to-yogurt connection.
The Lab
Dairy Chemistry
Elements that matter in your vat — Ca²⁺ in casein micelles, H⁺ and pH, S in β-lactoglobulin, Cl in sanitizers. Filterable periodic table with dairy-specific notes.
Coming soon
Osmosis & Ultrafiltration
The physics of membrane separation — osmotic pressure, flux, rejection rates, and how your UF system concentrates protein.
The Burn Book
for your eyes only
MAT 172
Meet the Plastics
A completely unbiased account of all 9 trig functions and their behavior. "sec is just cos in a trench coat." "it's giving unrequited." Petty. Accurate. Do not share with the x-axis.
BIO 111
The Osmosis Burn Book
Water cannot mind her business. A completely unbiased account of why osmosis is so annoying. "the membrane is doing group project labor." Do not leave unattended near a semipermeable membrane.
BIO 111
The Pathogen Burn Book
Salmonella, Listeria, C. botulinum (and Botox), E. coli O157:H7, Yersinia pestis, HAV, Norovirus, and Cryptosporidium. A completely unbiased account. Do not share with the pathogens — they already know what they did.
The Scrabble Playbook
just for fun
Why is OSHA Here?
process safety
BIO 111 — Biology
14 tools
BIO 111
Interactive Periodic Table
All 118 elements — clickable for details, filterable by category, searchable by name or symbol. Includes biological roles for every element.
BIO 111
Life's Building Blocks
CHON + minerals — the elements that make biology possible. Four tiers from the big four to trace elements, with body percentages and biological roles.
BIO 111
Elements by Biological Role
All 118 elements sorted by what they do biologically — essential macrominerals, trace elements, medically important, toxic, and not biologically active.
BIO 111
The Scientific Method
All 6 steps with real-world examples, key vocabulary, and the hypothesis branch — what happens when results say yes or no.
BIO 111
HeLa Cells & Scientific Ethics
The story of Henrietta Lacks, informed consent, the Belmont Report, and why it still matters today. Timeline, ethics principles, and vocabulary.
BIO 111
Properties of Life
All 8 properties with examples and edge cases, plus an interactive "Is it alive?" quiz — virus, fire, crystal, mule, coral and more.
BIO 111
Famous Organisms
8 prokaryotes and eukaryotes that changed science — from the bacterium in your yogurt to the worm that survived a Space Shuttle disaster.
BIO 111
Cell Structure
Clickable animal, plant, and prokaryote cell diagrams. Compare cell types side by side — prokaryote vs. eukaryote, plant vs. animal.
BIO 111
Chemistry of Life
Macromolecules, pH interactive scale, water properties, and chemical bonds — the chemistry foundation for everything else in bio.
BIO 111
Trophic Systems & Ecology
Trophic pyramid, cascades (salt marsh + Yellowstone), top-down vs bottom-up, food web, and microbial ecology including bacteriophage in dairy.
BIO 111
Phylogenetic Tree of Life
Clickable tree from LUCA to mammals, how to read phylogenies, 4 billion years of history, and the full classification system with your organisms.
BIO 111
Atoms, Isotopes, Ions & Molecules
Interactive atomic structure, isotope explorer, ion formation, and the three types of chemical bonds — the chemistry foundation of all biology.
BIO 111
BIO 111 Quiz
Flashcards + multiple choice across all BIO 111 topics. Filter by subject, shuffle, get immediate feedback on every answer. 70+ questions.
BIO 111
Energy & Metabolism
The full cellular respiration pathway — glycolysis, Krebs cycle, electron transport chain, and fermentation. Includes the yogurt-to-muscle lactate connection.
Coming soon
DNA & Genetics
Replication, transcription, translation — the central dogma visualized. Mitosis vs. meiosis and Mendelian genetics.
Coming soon
Evolution & Natural Selection
Darwin's theory, evidence for evolution, population genetics, and speciation — how life changes over time.
Coming soon
Body Systems
Digestive, circulatory, immune, nervous — how organ systems work together to keep you alive.
Quick reference
Download separately
Summer Agenda
June & July calendar with assignment tracker and study hours log. Available as an Excel file.