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Learn Trigonometry Fast

(from someone who can actually explain it)

Chris is a Stanford-educated tutor with over 10 years experience tutoring Trigonometry to students of all abilities, from students struggling to get from a C to a B, to go-getters trying to move an A- up to an A, to struggling students just hoping to pass. In that time he got a lot of experience learning how to explain this stuff in a way it actually makes sense to normal people. Through his videos he has helped countless students, and he can do the same for you.

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Unit Circle Chart
(click for FREE printable PDF) 
Bowtie Angles Chart
(click for FREE printable PDF) 

Trigonometry

  1. I. SohCahToa & The Unit Circle

  2. SohCahToa: Intro to Sine, Cosine & Tangent

    With this chapter we'll start trig off on the right foot -- triangles -- which has worked great for my tutoring students over the years. Also covered: what SohCahToa is; what opposite, adjacent, and hypotenuse mean; how to find sine, cosine and tangent; and how to work a bunch of "solving triangles" problems.

  3. Intro to Special Triangles

    In this chapter we'll get into the 30-60-90 and 45-45-90 triangles, with special emphasis on how to find their sides, do SohCahToa on them, and not get confused between which is which. Also, some super-tricky examples for students with tough teachers.

  4. Secant, Co-Secant, and Co-Tangent

    These new trig functions are just the reciprocal (flip) of sine, cosine and tangent, but they can be confusing, so we'll emphasize always writing them in the correct order each time, and we'll do lots of examples. I'll also show you how to do these on your calculator, which doesn't have buttons for these.

  5. The Unit Circle

    The longest chapter in trig. We'll start off slow, developing understanding by using SohCahToa to derive only the first quadrant of the unit circle at first. Then we'll work through reference angles, sign tricks, negative angles, co-terminal angles and undefined functions until you can calculate the six trig functions for any angle. We'll finish up with some tricks for memorizing the Unit Circle Chart.

  6. Radians

    Now that you've learned the Unit Circle in degrees, we're ready for Radians. This chapter the radian version of everything: reference angles in radians, negative angles in radians, etc. I also demonstrate common test problems like converting radians to degrees and degrees to radians, finding the six trig functions of angles with radians, and tricks for memorizing the radian unit circle.

  7. II. Formulas, Equations & Identities

  8. Sin-1, Cos-1 & Tan-1 a.k.a. "Inverse Trig Functions"

    Also called Arcsin, Arccos, Arctan, etc., these are problems like sin-1(1) where they give you the sin/cos/tan of an angle and you're supposed to give the angle in the correct quadrant. Key for solving trig equations, I explain how to do these with the unit circle or a calculator.

  9. Solving Trig Equations

    Trig equations are problems where you're solving for X or Theta but they're hidden behind a trig function, like "2sinX-1=0" or "tan2X-1=0". Lots of vocab in this one -- specific solutions, general solutions, 2npi, 360n -- and lots of factoring to do too. Easy to get confused between these and inverse trig functions!

  10. Trig Proofs & Identities

    Proofs strike fear in many a heart because most students were traumatized by proofs in Geometry. But have no fear. In this chapter I'll show you how to easily memorize the key identities you'll need, as well as take you through the Big Three techniques that will help you spot and solve most proofs.

  11. Lots of Formulas: Double, Half, Sum & Difference

    Double-angle, half-angle, sum, difference, even-odd properties... I cover all the odds and ends here in one place. Most of these you'll never see again, so I focus on getting you through it quick so you can move on.

  12. Power Reducing Formulas for Sine & Cosine

    Two trig identities which reduce a sin^2 or cos^2 to first-order expressions, a key skill for calculus.

  13. III. Graphing Trig Functions

  14. Graphing Sine & Cosine Functions

    These problems are frustrating for students because they pretty much all look the same, yet you can lose big points if you get one little shift or label wrong. Plus there's the annoying vocab: Amplitude, "b", phase shift, vertical shift. No worries, the videos in this chapter will sort it all out using explanations and techniques my students have found helpful, and I'll point out common errors to avoid.

  15. Graphing Tangent, Cotangent, Secant & Co-Secant

    I put these four in a separate chapter from Sine & Cosine for two reasons. First, many non-honors students don't even have to do these, so why scare you. Second, you should really get good at sine & cosine graphs first, since these four badboys are way easier if you base them on sine and cosine graphs, which is the approach I find helps students the most.

  16. IV. Applications of Trig

  17. Laws of Sines & Cosines

    Earlier in Trig, we've already had a few videos about solving right triangles for missing sides, so how is this chapter different? It no longer has to be a right triangle! These problems are way more complicated than SohCahToa, yet in this chapter students often seem relieved to actually be "doing something" again rather than learning "a bunch of stuff you'll never see again".

  18. Vectors

    Basics of vector addition, subtraction, multiplication, dot product, scalar product, magnitude, unit vectors, cross multiplication, and components.

  19. Parametric Equations

    This chapter covers converting parametric equations to rectangular and back again, eliminating the parameter, parametric forms of circles and ellipses, and graphing them.

  20. Projectile Motion
    (Pre-Calc Version)

    This chapter covers kinematics projectile motion problems as you would see in Pre-Calculus or Algebra 2 math classes. This topic is covered in more depth on the physics page. One-dimensional and two-dimensional gravity problems, range, vector components of velocity, etc.

  21. Arc Length & Sector Area

    This chapter covers the basics of arc length and sector area, as well as difficult word problems about bike gears, vehicle speed, planets, and velocity of rotating objects.

  22. Polar Coordinates

    This chapter covers everything from graphing polar coordinates and functions to converting equations between polar and Cartesian x-y coordinates. Also, how to do these on your calculator!

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