This looks like a mess because what you see here is a the end of a Trig lesson but it started off with just the triangle the jet and the numbers that you see in blue the 36 degrees and the 7,000. But as we talked about it and all the different ways we could go about solving for the numbers we didn't know more and more got written down so it looks complicated. It isn't. Once concepts are understood students generally go from F to A in short order. Here is a page on trig showing one such student.
What you see are actually THREE ways to go about finding answers, using Sin, Cos and Tan depending on the angle you use what function you use to give you the side you are trying to find.
instead of rectangles.
In fact trig is so easy that I built a page with lessons on it designed to show you how to teach trig to eight year-olds. Yes you read that correctly. Eight. Years. Old.
In this video they are doing trigonometry and having FUN doing it. Here is a video showing a lesson with two students...who don't know this is supposed to be hard and that quite few students twice their age fail this pretty regularly in high schools and colleges around the nation. If you are intimidated or lost then maybe you need to take a few steps back and check some of my other pages, but the point is any kid can do this even a grown up kid like you...and I show you how starting from step one. Here you see us AFTER we've been playing for a while because I want to show you what's possible.
Once we've played for a while and have gotten comfortable with the concepts and know when to divide and when to multiply and what function to use and the definitions of those functions the math itself is pretty easy, especially if we employ a calculator, but--and this is rather important, it's crucial to have enough "number sense" and understanding to know whether the number you got after you punched your calculator makes sense and isn't ridiculous. Sometimes you hit the wrong key...sometimes to divide when you are supposed to be multiplying and sometimes you may set the problem up incorrectly...so using a rectangle to clarify your thought at first can be quite useful.
These students are past that point. But I drew it in so you can see it applied to these problems. The students in the video already have played enough with these concepts so that these rectangles are understood. Algebra and trigonometry go hand in hand because algebra is man's greatest labor saving device. Coupled with multiplication math becomes easy to understand and learn because we aren't bogged down in computation or slowed down by basic problem solving. This way we can focus on CONCEPTS, and trigonometry becomes child's play.
Then we can ask very simple questions like how fast in the UFO flying in miles per hour and what is it's ground speed in miles per hour starting with just this much information:
|A UFO takes 5 seconds to reach a height of 1 mile taking off at a 58 degree angle in a straight line. How fast is the UFO going and what is it's ground speed?|
Remember I gave this problem to an eight year old. Now I will grant you that this is a "gifted" eight year old but I've taught this to other not so gifted eight year olds also, just takes a little longer which means we have to play more. So take a moment and do the math...if an eight year old can do it so can you or your teens. But start at the beginning...it has taken us multiple lessons to get this far...this didn't happen on day one. The same way they won't be speaking in Spanish sentences after a lesson or two in Spanish.
For a measly forty bucks I can teach you how to teach (just about) any "regular non-gifted" eight year old to do this too. No tears. No fear. Just fooling with math. If you actually buy a LIFETIME password you will find the trig page alone is pretty much worth the price of the password. Seriously.
And with a lifetime pass you not only get "How To Teach Trig To An Eight Year Old" you also get The Trig Page and a bunch of other pages that make teaching and learning math EZ too. How To Teach Trig To An Eight Year Olds is a "stand alone page" that comes with some added bonuses that you get with a full blown password and it also comes with some pdfs to get you going. So if you Don't have 350.00 bucks for a password or want to pay 37 bucks a month for 10 months and just want help with Trig just pay 40 bucks once and you are into that page for life. No expiration. And I think you will see that for 40 bucks you get a whole lot more than you are used to getting for 40 bucks.
What I have found over the years is that a lot of kids that come to me for trig help don't know basic algebra concepts and don't even have their multiplication tables down pat. Of course they are having trouble with Trigonometry and are confused. Couple with that with text books and their proclivity for starting in the middles and expecting you to have some serious perquisites under your belt and you end up with a lot of anxiety confusing and failing grades. You need to be able to identify a rectangle count to nine and tell if something is same or different or not to get started with me.
There is no need for fear or failing grades. Forty bucks will make all the difference. Don't believe me though, no brochure makes the hotel look bad. Go read what some other people have got to say. Skip Starbucks 8 times and you can change your kid's life forever.
Click on the links to the trig pages and you will find FREE lessons there.