Math's Trig Versus Basic's Trig Functions

[bplus]

Remember Obamacare? That's why Democrats can't do simple math... because there are no left triangles!

That explains why they're always looking for a bigger slice of _PI, but we're going off on a TAN here...

Yah, a little comic relief is OK. Getting back:

I think a lot of folks resist trig because of the amount of memorization that's required. I know it's the case with me. I only discovered the SOH CAH TOA mnemonic a few years back. It certainly wasn't taught to me in school. Prior to that, anytime I needed to use trig it was off to find a math book or my machinist notes. It was only a few days ago that I found that with the reciprocal identities, only one of each pair starts with "CO..." So now I no longer need confuse which is secant and cosecant.

SOH, CAH, TOA ? is that Klingon? Sin Cos and Tan are the main players that must be the S, C, T that start you mnemonics.

This is how I learned these Ratios, yes remember that first they are Ratios of lengths of sides:

Hypotenuse is the length of the longest slanted line opposite the Right Angle.

Now the triangle has 2 other angles so pick one and call it the Angle being considered so:
Then there are 2 sides lengths named: Opposite the Angle being considered and Adjacent the Angle being considered.
   Sin = O/H "Opposite Over Hypotenuse"  Opposite Over Hypotenuse is the side opposite the Angle being considered 
   Cos = A/H "Adjacent Over Hypotenuse"  Adjacent is the side next to the Angle being considered
   Tan = Sin/Cos = Opposite/Adjacent O/H

So then for the other angle not being considered it's Sin and Cos are just the reverse of the Angle being considered so it's Sin is the other angles Cos and it's Cos is the other angles Sin. But if that gets confusing drop it, don't need to memorize that because so easily figured out later.

Then I just lookup Secant is the reciprocal of Cos so for 1/Cos Algebra reverses top and bottom numbers for H/A, laughs I guess; and CoSecant is the other one. H/O  H/A and H/O very funny stuff! ;-)) (Trying hard not to get boring like a machinist.)

Hey @OldMoses you were a machinist too! I wasn't a machinist per say but learned to program a CNC lathe for fasteners (threads for screws as well as regular "turnings") manufacturing companies. So I had the lowly title of Machine Operator.