Math's Trig Versus Basic's Trig Functions

[OldMoses]

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.

Probably a Hawaiian/Klingon dialect. 

SOH = Sine is Opposite over Hypotenuse
CAH = Cosine is Adjacent over Hypotenuse
TOA = Tangent is Opposite over Adjacent

I do machinist stuff on the farm, but wouldn't deign to call myself a "machinist" per se. It started as a hobby. I've got two main lathes, a '47 Logan 820 and a post WWI Monarch model "A", as well as a couple project lathes. I also have a Hendey Norton mill from approximately the same era as the Monarch. www.plainviewfarms.com/mill  shows my rehabilitation of that machine. I also rescued and cleaned up an 1881 E. Gould and Eberhardt Shaper. That's by far my oldest piece. One of the main uses for trig in hand operated machines is for setting lathe compound rests to do threading and precision feeds. I've also used it to plot locating moves for milling indexing plates.

I've cut threads and built things like bushings, simple worm drives and hydraulic manifold blocks. Mostly though it's attachments for the main machines like carriage stops, spindle indexers and other sunderies. We do some millwright type welding and fabrication work and associated stuff as well to keep things percolating on a farm with an eclectic mix of ancient and modern equipment. If there's something that we need that's either not made, or not available, I'm generally on the case around here. As such I'm constantly running into problems that trig is the easiest method to solve. I've used it for years, like a little old lady uses her car, but only recently have I made an in depth study of how it really works.

I really don't know why this post is spaced out so much, I can't seem to get rid of it, sorry...