quote:

Old Dino said - PHPaul ... what is your end game in learning Trig ? Something needed as a job requirement or something to learn for daily use ?

Partly just as an intellectual exercise, partly for practical usefulness.

For fabrication, determining the diameter of a circle from a known arc or segment has come up several times.

Being able to get a good estimate of the height of an object from a base line and one angle would come in handy fairly often as well.

I've ordered used "For Dummies" text and workbooks as a starting point.

Trig is the gateway for many, many practical applications and higher math. Being able to visualize sine, cosine, and tangent is a quantum leap in math knowledge. Knowing why and how force or speed vectors are dependant on sines and cosines is mind-expanding. As others have mentioned, plane geometry knowledge is required for trigonometry. By "knowledge" I mean knowing it inside and out.

The highest math course I fluked in Aerospace Engineering was misleadingly named "Applied Mathematics". When the only woman in the class verbally substituted trigonometric functions in a differential equation, on the fly, I knew I was doomed.

quote:

Originally posted by cne32507:
Trig is the gateway for many, many practical applications and higher math. Being able to visualize sine, cosine, and tangent is a quantum leap in math knowledge. Knowing why and how force or speed vectors are dependant on sines and cosines is mind-expanding. As others have mentioned, plane geometry knowledge is required for trigonometry. By "knowledge" I mean knowing it inside and out.

I'm fairly confident in my grasp of plane geometry. I may find out otherwise when I get into it, but we shall see.

I love the "For Dummies" books ... have on many different subjects. Like how they explain in plain English.

quote:

Originally posted by TRIO:
The best thing I learned was about trigonometry was an Indian named "Soh Cah Toa". That, along with the 3,4,5 triangle example.

This might not be politically correct now, but it sure helped me a lot.

Must be New Math. I had Trig in 1954 and never heard of Soh Cah Toa. However, I'm guessing it is a way of remembering which sides of a triangle are involved in the Sine Cosine Tangent of an angle: "o" = side opposite; "a" = side adjacent; "h" = hypotenuse ? (In my day, we didn't use a memory aid--we just used our memory.)

Regarding the Taylor expansion series used to calculate the Trig functions, I programmed in COBOL for many years. COBOL is a great language (still) for business purposes, but it is very limited in math functions--it only has add, subtract, multiply, divide, and raise to a power--no Trig functions. I once had a need to use logarithms in a program, so I wrote a subroutine to use the Taylor expansion to compute them. I noticed that the same elements in the expansion were used in calculating the Sine and Cosine, but with different patterns of signs, so I expanded my subroutine to also calculate the basic 6 Trig functions, too. Years later I actually had a need in a COBOL program to use one of those Trig functions. I was prepared!

flashguy

quote:

Originally posted by flashguy:
Must be New Math.

Thanks. I had no idea what that "Indian" name referred to.

I’ve written some instructional material discussing wind values and the effective speed of targets moving at angles other than 90 degrees, and make reference to the sine (sin) of the angle. I sometimes wonder how many people would so much as recognize the terms, much less why they apply. Someplace I saw something to the effect that if we wanted boys to become enthused about learning math, tell them that an understanding of trigonometry is essential for long range shooting. It isn’t, of course, not for all of it anyway, but I still remember that it was the practical applications of math that always engaged me.

quote:

Originally posted by sigfreund:

quote:

Originally posted by flashguy:
Must be New Math.

Thanks. I had no idea what that "Indian" name referred to.

I’ve written some instructional material discussing wind values and the effective speed of targets moving at angles other than 90 degrees, and make reference to the sine (sin) of the angle. I sometimes wonder how many people would so much as recognize the terms, much less why they apply. Someplace I saw something to the effect that if we wanted boys to become enthused about learning math, tell them that an understanding of trigonometry is essential for long range shooting. It isn’t, of course, not for all of it anyway, but I still remember that it was the practical applications of math that always engaged me.

I always enjoyed doing the "Identity" proofs in Trig; however, my versions, although correct, were often a few steps longer than the approved ones.

I struggled with basic Algebra in high school, but eventually the dawn broke and I was successful. I breezed through Plane and Solid Geometry (and dragged 2 female cousins through it), and loved Trig. In college I went as far as Partial Differential Equations (but did not do well in that discipline--ordinary Diff was OK, though). I've never used any of my college math in my life, but don't consider it a waste of time.

During my college years I worked 2 summers for a large surveying firm in Detroit. My job included doing a lot of Trig calculations while "proving" surveys. I used 10-place Trig tables and a Friden electric calculator with a 20-place carriage. It did not have the automatic square root function, so I had to learn a procedure to extract a square root using only the basic functions of the machine (there is one, and it is accurate, though arcane).

flashguy

...
I used 10-place Trig tables and a Friden electric calculator with a 20-place carriage. It did not have the automatic square root function, so I had to learn a procedure to extract a square root using only the basic functions of the machine (there is one, and it is accurate, though arcane).
flashguy[/QUOTE]

My mother had a Friden in her classroom (she taught accounting).

In the 1980's one of my coworkers asked how to find a square root using the old paper method we learned in the 8th grade. He asked for his school-age daughter. I didn't remember how to do this so I called the local university's math department. The prof. who was connected didn't remember either. He did, however, explain a quotient averaging method using a simple electronic calculator (that didn't have a sq root key). I had never heard of this either! In college, we just used our slide rule. The quotient averaging was quick, easy, and accurate.

I have never heard of the Taylor method for trig functions. Again, we used our slip sticks.

I can remember sitting through one of the weeks of USN gun fire control school during the '60s. We had to use Vector Mathmatics in conjuntion with Trig to solve the gun barrel angles to hit moving targets. It was interesting but not practical to use in a live shooting situation. Thank God for computers that do that for us, even back then.

This message has been edited. Last edited by: yanici,

quote:

Originally posted by PHPaul:

quote:

Originally posted by HRK:
Why Trig, what's your angle?

Don't be obtuse.

Ok guys, we are getting off on a bit of a tangent here.

quote:

Originally posted by Graniteguy:

quote:

Originally posted by PHPaul:

quote:

Originally posted by HRK:
Why Trig, what's your angle?

Don't be obtuse.

Ok guys, we are getting off on a bit of a tangent here.

It's a cute pun.

quote:

Originally posted by cne32507:
...
I used 10-place Trig tables and a Friden electric calculator with a 20-place carriage. It did not have the automatic square root function, so I had to learn a procedure to extract a square root using only the basic functions of the machine (there is one, and it is accurate, though arcane).
flashguy

My mother had a Friden in her classroom (she taught accounting).

In the 1980's one of my coworkers asked how to find a square root using the old paper method we learned in the 8th grade. He asked for his school-age daughter. I didn't remember how to do this so I called the local university's math department. The prof. who was connected didn't remember either. He did, however, explain a quotient averaging method using a simple electronic calculator (that didn't have a sq root key). I had never heard of this either! In college, we just used our slide rule. The quotient averaging was quick, easy, and accurate.

I have never heard of the Taylor method for trig functions. Again, we used our slip sticks.[/QUOTE]The accurate algorithm/procedure using a Friden calculator to do square roots is somewhat based on the fact that the sum of consecutive odd numbers is always the square of the number of terms (1 + 3 = 4 = 2²; 1 + 3 + 5 = 9 - 3²; etc.) and involves subtracting odd numbers with arcane carrying procedures. If analyzed, the remainders at each step are the same as if one were using the manual method (pencil and paper), so it is accurate. However, when watching people using the procedure, it appears that they've gone crazy, with bells ringing and the carriage moving weirdly. It requires special setup of the machine, too--switching it so that subtractions are counted possitively and thqt the keyboard does not reset after each operation (keys stay down). I got good at it.

You can find the Taylor series here: https://www.math10.com/en/univ...s/taylor-series.html scroll down to the Trig functions. "x" is the angle in radians. It is easy to write a subroutine to perform those iterations.

flashguy

Using the Trig sections of a welding handbook or a Martin Sprocket book helped us with our plant projects.

Not trig related but, one of the coolest darn sorta math related posts I've ever read in Sig Forum goes back just a few years. Some of you will recall. IIRC, it was a prop of a P51 Mustang fighter, in a photograph. Some how, flashguy new the idle speed of that particular Mustang engine, and there were at least 2 different engines, he determined the shutter speed setting of the photographers camera.. . That will stick with me for the rest of my days flashguy..

quote:

Originally posted by David Lee:
Not trig related but, one of the coolest darn sorta math related posts I've ever read in Sig Forum goes back just a few years. Some of you will recall. IIRC, it was a prop of a P51 Mustang fighter, in a photograph. Some how, flashguy new the idle speed of that particular Mustang engine, and there were at least 2 different engines, he determined the shutter speed setting of the photographers camera.. . That will stick with me for the rest of my days flashguy..

I remember the post, but I'm not able to find it with a search of this forum.

flashguy