Thinking about graphing on a coordinate plane, slope and other analytic geometry.
Functions and their graphs
Revisiting what a function is and how we can define and visualize one.
Polynomial and rational functions
Exploring quadratics and higher degree polynomials. Also in-depth look at rational functions.
Exponential and logarithmic functions
An look at exponential and logarithmic functions including many of their properties and graphs.
Trig identities and examples
Parametric equations and polar coordinates
An alternative to Cartesian coordinates.
A detailed look at shapes that are prevalent in science: conic sections
Systems of equations and inequalities
What happens when we have many variables but also many constraints.
Sequences, series and induction
An assortment of concepts in math that help us deal with sequences and proofs.
Probability and combinatorics
Basics of probability and combinatorics
Imaginary and complex numbers
Understanding i and the complex plane
Hyperbolic trig functions
Motivation and understanding of hyperbolic trig functions.
Preview of the calculus topic of limits
Trig identities and examples
If you're starting to sense that there may be more to trig functions than meet the eye, you are sensing right. In this tutorial you'll discover exciting and beautiful and elegant and hilarious relationships between our favorite trig functions (and maybe a few that we don't particularly like). Warning: Many of these videos are the old, rougher Sal with the cheap equipment!
- Trigonometry identity review/fun
- Trigonometric identities
- Examples using pythagorean identities to simplify trigonometric expressions
- Pythagorean identities
- Proof: sin(a + b) = (cos a)(sin b) + (sin a)(cos b)
- Proof: cos(a + b) = (cos a)(cos b) - (sin a)(sin b)
- Trig identities part 2 (part 4 if you watch the proofs)
- Trig identies part 3 (part 5 if you watch the proofs)
- Cosine addition identity example
- Double angle formula for cosine example
- Addition and subtraction trig identities
This tutorial is a catch-all for a bunch of things that we haven't been able (for lack of time or ability) to categorize into other tutorials :(
- Navigation word problem
- Fun trig problem
- IIT JEE trigonometry problem 1
- IIT JEE trigonometric maximum
- IIT JEE trigonometric constraints
- Trigonometric system example
- 2003 AIME II problem 11
- 2003 AIME II problem 14
- Trigonometry word problems (part 1)
- Trigonometry word problems (part 2)
- Ferris wheel trig problem
- Ferris wheel trig problem (part 2)
The primary tool that we've had to find the length of a side of a triangle given the other two sides has been the Pythagorean theorem, but that only applies to right triangles. In this tutorial, we'll extend this triangle-side-length toolkit with the law of cosines and the law of sines. Using these tool, given information about side lengths and angles, we can figure out things about even non-right triangles that you may have thought weren't even possible!