Trigonometry - Help?

[Tesla]

Hey everyone on GTPlanet, I was wondering if someone could help me understand trigonometry. Whenever a question comes up in my maths classes, I have no idea how people get to the answer. What are the basic concepts of it and how would they be applied to questions in tests and such?

 

[Small_Fryz]

You really need to post an example question of what you are trying to do. Are we talking basic trig or?

 

[Tesla]

Year 9 level. So, something like this:



Finding x to 2 decimal places.

 

[Omnis]

The key to trig: SOH CAH TOA. Remember that. Look it up on google.

In your example, we have a hypotenuse, an angle, and the side opposite of the angle. So we'll use SOH, or sine, opposite, hypotenuse.

Sine of the angle = opposite side length over hypotenuse.

Sin(40 degrees) = 41/X. Plug into your calculator (make sure it's in degree mode).

http://www.wolframalpha.com/input/?i=sin(40deg)=41/x

 

[Tesla]

Oh, I think I get it now. So if I put Sin(40 deg) into my calculator, it should give me my answer?

 

[Omnis]

No, it will give you the sine of 40 degrees, which is a ratio. Sin(40) will give you the left side of the equation, and then you'll have to solve for x using regular algebra.

Sin, cosine, and tangent are all special functions which are simply the ratios of certain sides of a right triangle. In your example, you're looking for an x to make 41/x match the sin(40) ratio.

I always thought they should teach basic trig much earlier than they do. It's really much simpler than it looks.

 

[Small_Fryz]

I use this btw. Learnt it almost 10 years ago and still remember it.

Some Old Hags Can't Always Hide Their Own Age.
SOH / CAH / TOA

 

[Tesla]

Ah, now I understand you Omnis. And for the record they introduced us to trig when I was in year 8, but it was only a lesson or two which I missed due to being overseas.

 

[Azuremen]

Some Old Hags Can't Always Hide Their Own Age.
SOH / CAH / TOA

Some Old Hippie Came Around Here Tripping On Acid.

That is how I remember it anyhow.

Sin(angle), Cos(angle) and Tan(angle) give fraction or decimal values that are the ratio of different sides of the triangle relative to the angle in question.

In this case, Sin(40deg) * x = 41.

Rearrange to solve for x,

x = 41/(sin(40deg))

Of course, this is for right triangles - ones which contain a 90 degree angle.

 

[Shaun]

Tesla, as Omnis said once you get the knack of it, basic trig isn't that hard and it's very usefull.
It isn't one of the things you will learn in school that you think you will never use again.
An example, I built a pergola a couple of years ago and how do you think I worked out the timber lengths that incorporated various angles? Yep basic trig.
Take your time to learn it mate, you will use and benefit from it in the future at one stage.

Cheers Shaun.

 

[Omnis]

Soh cah toa is the only mnemonic you need.

 

[Leicht]

WOW, how old are you btw? I'm certainly not missing my year 12 maths anymore

 

[ECGadget]

Yeah, always remember SOH CAH TOA. It comes in handy a lot!

 

[Ross]

I remember it as "Silly old headmaster cancelled all holidays to our amazement"

 

[NissanSkylineN1]

Isn't SOH CAH TOA some Native American prince?

 

[Tesla]

Sounds like an Indonesian island to me.

 

[dylansan]

My calc professor always makes fun of people "praying to the SohCahToa god" during his tests. He always hears kids quietly chanting the phrase in the hopes that the trig god will be merciful.

He decided to teach us a different method, in case people lost faith in SohCahToa. It involves writing the first letter of the trig function in cursive around a triangle and dividing the first stroke into the second stroke. Of course, the triangle has to be in the same orientation every time, so it might not be that useful.

After a while you won't need a mnemonic, anyway. You'll just start getting used to sine being opposite, cosine being adjacent, and tangent being both. And when you start using them for things like x and y components of circles, it will become even more ingrained in your mind.

 

[NissanSkylineN1]

Tesla, I actually learned Trig not too long ago, and guess where I went that helped me the most. Khanacademy.org They have practise questions and videos. Its really great. Here's some of the videos. Be sure to check out www.khanacademy.org for the practise questions (its an NGO too).

 

[wfooshee]

I was in trig so long ago I think it had just been invented. We were taught that SOHCAHTOA was an "Indian" (i.e. native American) chief's name. How's that for pre-"politically correct?"

Omnis's "Camp Soh-cah-toa" is close to that.

 

[CMvan46]

Soh cah toa is the only mnemonic you need.

Yup just remember that. Just always remember it's sine(opposite/hypotenus), cosine(adjacent/hypotenus), and tan(opposite/adjacent). You can't just plug in the one thing you know in the bracket or you'll get the wrong answer.

I hope they've shown you basic algebra first so that you can isolate your unknown otherwise you should go in and ask for help in person.

 

[Schwartz]

Trig is very easy once you understand it. Its basically just plugging in numbers. You're in for a few easy weeks in class... If you understand it...

 

[ROAD_DOGG33J]

Soh cah toa is the only mnemonic you need.

What about Cho sha cao?

 

[dylansan]

Not necessary if you know the cofunctions are just the inverse of the regular ones.

 

[Joel]

We always learned the cofunctions as SYR CXR TYX (Sir Kickser Ticks).

 

[Azuremen]

We always learned the cofunctions as SYR CXR TYX (Sir Kickser Ticks).

Working on that unit circle, I see. Once you start applying it and mixing and matching with Calc and other related things, it just kind of becomes second nature.

 

[Crispy]

Just did the question triangle question on my calculator, X would be 55 correct?

 

[AlexGTV]

1. Know the Pythagorean Theorem

2. Know what a radian is: arc/diameter or "how much of a turn" where a whole turn = 2π*hypotenuse (radius), and because in trig. the hypotenuses for simplicity is taken one 1, then one turn = 2π.

3. Know the definitions of sin, cos, tan. Nothing difficult, they are just ratios of right triangle sides.

The above is pretty much all of trigonometry.

 

[NissanSkylineN1]

What about Cho sha cao?

We need to make a story for that.... A Chinese Princess perhaps?

However, the reason why it wont work as well as SOH CAH TOA is that they've done it so its easy to write out the formula:

SOH - Sine= Opposite/ Hypotenuse

SHA - Sine= hypotenuse/Adjacent?

 

[Kylehnat]

Trigonometry is useless to 95% of the population, but it's everywhere in engineering. Praise the SOH CAH TOA god every time you drive across a bridge .

 

[dylansan]

We need to make a story for that.... A Chinese Princess perhaps?

However, the reason why it wont work as well as SOH CAH TOA is that they've done it so its easy to write out the formula:

SOH - Sine= Opposite/ Hypotenuse

SHA - Sine= hypotenuse/Adjacent?

CHO - Cosecant = Hypotenuse/Opposite (1/sine)
SHA = Secant = Hypotenuse/Adjacent (1/cosine)
CAO = Cotangent = Adjacent/Opposite (1/tan)

It's still easier to just know which cofunctions go with which regular ones than to have another mnemonic to get confused with.