If you're in pre-calculus, trigonometry is an important topic! And within it are many new functions, like sine, cosine, tangent, and other such things. What do these mean?! Don't worry, in this short 11-part series, we will hit all the major points so that everything will make perfect sense!

Alright, it's time to get into some more challenging math! Trigonometry is a subject that many people find intimidating, but once you understand some new ways to look at angles and some functions that pertain to them, it's really not so bad! First things first, let's make sure we understand what a radian is, and how to measure angles using them!

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OVERSEAS

Introduction to Trigonometry: Angles and Radians

There are tons of formulas we can learn that involve trigonometric functions. These help us evaluate trig functions for angles that are half of a common angle, twice a common angle, the sum or difference of two common angles, all kinds of stuff. They are a little annoying to learn but they are super useful so let's just bite the bullet and knock them all out in one clip!

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Formulas for Trigonometric Functions: Sum/Difference, Double/Half-Angle, Prod-to-Sum/Sum-to-Prod

The law of sines helped us solve for all the sides and angles in SAA, ASA, and SSA triangles, but now we have to learn the law of cosines if we want to solve for SAS and SSS triangles. This one is kind of like the pythagorean theorem, just for oblique triangles instead of right triangles, so it has trig functions in it. Let's check it out!

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The Law of Cosines

This is the thing that has kept you up at night all week! That darn unit circle! So many roots and fractions and pies, how will you get it all in your head? Actually it's super easy to memorize the unit circle if you know a few tricks, so check this out and rest easy tonight!

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The Easiest Way to Memorize the Trigonometric Unit Circle

We love to graph functions, and now that we know about the trigonometric functions, let's learn to graph those too! These are periodic functions, meaning they spit out the same values over and over and over, with a frequency that depends on the period of the function. This will be easy to understand if we have the unit circle memorized, so make sure you've watched that tutorial too, and then let's do this!

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Graphing Trigonometric Functions

All of these trig functions come in real handy for finding the sides and angles of right triangles, but what about oblique triangles? If a triangle doesn't have a right angle, SOHCAHTOA doesn't apply. What do we do?! Don't worry, there are other ways to use these trig functions with oblique triangles, and one of them is called the law of sines. This relates the sides and angles of oblique triangles, so let's make sure that we know how to use it.

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The Law of Sines

Now that we know what these trigonometric functions are, how do they relate to one another? In a variety of ways, in fact! There are lots of identities we will have to learn so that we can do algebra with trig functions later, so let's learn these now.

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Basic Trigonometric Identities: Pythagorean Identities and Cofunction Identities

We know about inverse functions, and we know about trigonometric functions, so it's time to learn about inverse trigonometric functions! These are functions where you plug in valid values that trig functions can possess, and they spit out the angles that produce them. There's a little more to it than that, so let's get into it!

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Inverse Trigonometric Functions

Verifying trigonometric identities can be super fun! And also very frustrating when you can't figure them out. It can be tricky because there's no precise way to go about doing this, you have to just use your intuition, but let's go over some common strategies and identities that will more than likely use at one point or another!

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Verifying Trigonometric Identities

We solved so many equations when studying algebra. Now that we understand trig functions, as well as inverse trig functions, we are ready to solve trigonometric equations. This will combine an understanding of trigonometry with some of the techniques we learned in algebra, and in the end, all we are doing is finding the value of x that makes the equation true, so it's nothing new!

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Solving Trigonometric Equations

Oh man, what is all this sine and cosine business? What do these things even mean?! And Greek letters now? I don't know Greek! OK friend, just relax. Understanding the trig functions is as easy as pi radians. We just make some triangles and set up a few definitions. I promise it's no sweat, just watch this!

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The Law of Cosines

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Trigonometry #11

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