Study Guide

Analytical Trigonometry

Analytical Trigonometry Introduction

We've been working part-time as a celebrity handler backstage at the Grammys. You know: making coffee, running errands, listening to their existential crises moments before the show starts, that sort of thing. We get to mingle with the stars, get a glimpse of the high life, and if we're lucky, we get a nice, fat tip. We're saving up for a jet-ski.

Celebs are getting more and more demanding these days, though. While one will request an all-white dressing room with roses and champagne, another is looking for a mountain of gummi bears, two dozen mannequins, and 10 cases of Red Bull. If we fail to meet these demands, we might as well start looking for a job.

Trigonometry is no different. It is a beautiful thing. It may be demanding and straight-up difficult at times, like our favorite celebrities, but it's still a beautiful thing. Once we learn to meet those demands and work with it, trig will help us do things we once thought impossible. Not owning a jet-ski, but other things. With trig, we can work with just about anything that has an angle in order to find missing angles, sides, areas, and more. Stick with us and you'll see what we mean.

Analytical Trigonometry Resources


Symmetry of Trig Functions
For a nice, slow, in depth approach to symmetry of trig functions, check this out. It gives visuals and some examples to work through in order to get more comfortable with what even and odd trig functions are.

Inverse Trig
This provides a good explanation of the domain restrictions on inverse trig functions and why we have them. It also gives a visual of what an inverse trig function looks like on a graph.

Trig Identities
A compilation of trig identities. This will save you from leafing through everything whenever you need to remember a formula.


Khan Academy Addition Formula Proof (and More!)
The addition formula for sine (and cosine, for that matter) can be pretty tricky to derive, so having a video handy is definitely a good idea. From here you can get to proofs of other identities too.

Using the Laws of Sines and Cosines
This goes more in-depth about when to use the Law of Sines and the Law of Cosines. It's always a good idea to know when to use things.

Graphing Trig Functions
This walks through how to graph a trig function. It also gives a good explanation of what all of the variables in the y = Asin(Bx +C) +D form mean on the graph.

Games and Tools

Online Graphing Calculator
This works just like a graphing calculator, but online. It also gives more information that you would probably ever want to know about the function being graphed, in case you are curious.

Trig Spinner
If you're looking for more practice with knowing the trig values of some basic angles, this will help drill it into you.

Trig Flashcards
If you thought you left flashcards behind when you left basic math (we're sure you long for the simpler days of 1 + 1 = 2), think again. There are flashcards for trig! It's good practice with finding trig values and inverses.

Quia Trig Identities Games
Here is a whole lineup of games/activities to help you memorize the trig identities. With some variety you can review in a few ways to really make sure you know them all.