Solving Trig Equations

Solving trig equations is a topic that hurts pretty bad if you're not already a master of the inverse trig functions, so if you aren't a master of those, might want to go to the inverse trig functions page to get some tutoring on that before you delve into trig equations. Otherwise (or if you're just in a hurry), take a gander at the videos below, as they will lead you through the land of factoring and trig equations with your pride (and hopefully grade) intact.

Solving Basic Trig Equations (without exponents)

This first video just covers how to solve basic trig equations with no exponents and nothing in front of the variable, such as 2cosX-1=0, sinX-2=0, and tanX=2. T The trick with these is to forget all that stuff you just had to memorize for inverse trig functions about which quadrants go with what: the whole unit circle is fair game!

"General Solutions" vs "Specific Solutions"(without exponents)

This video will answer a host of questions: What does [0,2pi] mean? Why "2npi" or "360n"? This is where you have to pay careful attention to whether they're asking for a general solution where you have to account for infinite co-terminal angles (thus the "n"), or just limit yourself to the unit circle other interval.

Solving Trig Equations on your Calculator

When trig teachers let you use a calculator for something, nine times out of nine it's a trap, and this is no exception! See, when you solve a trig equation on your calculator, your only choice is the inverse trig buttons. But guess what: those will limit you to only a couple quadrants! Teachers know this, hence the trap. In this video, I'll show you how to deal with that and find the answers your calculator doesn't want to give you.

Solving Squared Trig Equations -- No Factoring

Putting an exponent on the sine or cosine makes trig equations twice as hard. In this video we'll work the slightly easier type where there is ONLY a squared trig function -- nothing to the first power -- which allows us to square root both sides: cos2X-1=0, sin2X-2=0, and one with no solution! In the next video on the trig equations page, we'll factor.

Factoring - Let's review!

If you're already a factoring master, feel free to skip this video. But if you haven't factored in a while you might want to watch it, since factoring trig equations is going to be twice as difficult as factoring with just x. For even more factoring practice, especially if you have a tough teacher, check out the Algebra 2 factoring page.

Solving Really Hard Trig Equations (with factoring!)

If you're lucky, maybe your teacher won't even make you do these, especially if you're not in honors. But for most kids, this will be the worst factoring problems you'll ever see. Stuff like sin2x-2sin+1=0, cos2x+2cosx-3=0, and 3tan2x-4tanx-5=0. (Notice I didn't say worst trig equations, because I'll reserve that honor for equations with a number in front of the x!)

What if there's a 2 or 3 in front of Theta/X?

These are the worst -- cos3X-1=0, sin2X-2=0 -- and they're typically for honors students only. Believe me, I hate these as much as students do, and it took me a long time to figure out a good way to explain them. Luckily, that was a while back, so you get the fruits of my experience on this one! Still no fun, but if you drop your 360n or 2pi(n) in at the right time, it becomes a plug-and-chug affair.

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