# Shop Math = Trigonometry or Bust



## Janderso (May 8, 2020)

I'm no math wizard but I am determined to relearn trigonometry.

I have found recently I need to prove/confirm my set-ups for milling and surface grinding.
I am looking for a compound sine plate and if I ever find one within my budget I plan on using it.

I stumbled upon Ray Galant's, Youtube channel. His handle is, Shop Math.

He has really helped me understand a few very important concepts.


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## higgite (May 8, 2020)

Ray's not bad at math, but his spelling could use a little work.  

Tom


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## Lo-Fi (May 8, 2020)

Khan Academy videos are excellent too if you want it covered from another angle (pun intended)


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## DavidR8 (May 8, 2020)

Also NancyPi


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## Janderso (May 8, 2020)

Hadn't been exposed to either of those sites, thanks.


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## benmychree (May 8, 2020)

I was a poor math student in school, even with tutoring; algebra made no sense to me, but trig was easier because you could see the physical shape of things, if I can find the formula in machinery's handbook without having to rehash it (algebra deficiency) I could work out a problem.  My use of it is mostly confined to figuring approximate leads of spirals for the milling machine in cutting mostly spiral gears, I try to determine the spiral angle of the sample gear and from that come up with an approximate lead of spiral, consult the B&S book with a table of spiral leads, set up a gear train and with the sample gear in place on the dividing head, use a DTI to detect whether the spiral is too fast or slow, and set up other gear trains until I get it right on, usually this may take only several tries.  The spiral angle is measured on the pitch diameter, something that is not really easy.


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## 4ssss (May 8, 2020)

Why bother.   I learned Trig in Trade School and haven't used it since. That's why Engineers' make the big money.


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## Janderso (May 8, 2020)

Sounds very complicated.
My favorite math problems were in geometry for the same reason, you can see the problem and work it out.


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## Janderso (May 8, 2020)

4ssss said:


> Why bother.   I learned Trig in Trade School and haven't used it since. That's why Engineers' make the big money.


It's one of those things that is lost if you don't use it. Speaking for myself of course.


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## Lo-Fi (May 8, 2020)

Khan Academy got me through some pretty heavy vector maths when writing a game expansion (Google my forum name and Kerbal Foundries if curious). 3Blue1Brown if you're in the mood for advanced Calculus.

That all being said, I don't do trig manually myself any more. If I need to work something out, I draw it up in a 2D cad sketch and get the computer to do the heavy lifting for me. It's literally impossible to get the wrong formula or have a brain fart with the calculator. I can even do this on the Onshape phone app! 

Its funny: "you don't always have a calculator with you" was a phrase often thrown around to encourage manual calculation when I was in school... 

Hold. My. Beer. 

Brushing up on an overview of trig it is great, but further than that, time could be better spent learning a cad package. In my humble opinion. 

I use CAD literally all the time in my shop. Not that I draw everything up in 3D - often it's simple 2D stuff like hole patterns. Great example is T nuts: I wanted to knock four out of a single piece of stock. I could have manually calculated the hole spacing, giving allowance for saw cuts, cleanup etc.... It took me literally a minute to knock up a 2D drawing, which then allowed me to show dimensions from any datum. I defy anyone to do it quicker with pen and paper. More like using it as a truly graphical calculator in this context, and it works just as well for stuff you'd ordinarily need trig for: Draw your triangle. Dimension the bits you know. Click to display the dimensions you don't know and the solver does the heavy stuff in a nanosecond. Need to change it? Modify any dimension and everything else is automatically recalculated. Food for thought, anyway


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## Janderso (May 8, 2020)

Lo-Fi said:


> Khan Academy got me through some pretty heavy vector maths when writing a game expansion (Google my forum name and Kerbal Foundries if curious). 3Blue1Brown if you're in the mood for advanced Calculus.
> 
> That all being said, I don't do trig manually myself any more. If I need to work something out, I draw it up in a 2D cad sketch and get the computer to do the heavy lifting for me. It's literally impossible to get the wrong formula or have a brain fart with the calculator. I can even do this on the Onshape phone app!
> 
> ...


What CAD program would you suggest?
FMC 360 is just too hard for my little bird brain.


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## Mitch Alsup (May 8, 2020)

4ssss said:


> That's why Engineers' make the big money.



Engineers work on solving problems their entire lives.
That is why we get to retire early and work in our own shop(s).


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## Mini Cooper S (May 8, 2020)

This chart has served me well for 50 years. I originally found this in a Lufkin tool catalog. Everything you need to know about shop trig, but were afraid to ask!


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## GunsOfNavarone (May 8, 2020)

I highly recommend
Kahn Academy

You pick your level and pace, it stores where your at to pick back up, tests you...everything. I had the same need as O.P.


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## westerner (May 8, 2020)

I got decent grades in math, but did not use much of it for so long I have forgotten many critical principles.
Lazy fellow that I am, I simply downloaded a "Triangle Calculator" app for the phone. Never without it, and it is always SURE which equation to apply.....


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## Tozguy (May 9, 2020)

Back in 1963 at technology school we were shown how to use a slide rule and math tables. To this day I look up the values of trig functions in the same book of math tables.  No one dreamed about using a small portable wireless phone to replace all the books and professors we had at the time.


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## Suzuki4evr (May 9, 2020)

DavidR8 said:


> Also NancyPi


Any relation to joe pi.......?


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## HarryJM (May 9, 2020)

Math, beyond simple addition, division, multiplication, has always been a challenge for me as I generally like to learn new things that I can use and trig was not something that I found a use for until I started my metal working hobby and educating myself via this forum and YouTube.

The below Joe Pieczynski video for setting a lathe compound to precision angles is a good example of a lathe trig application and yes I had to watch it several times before it started to make senses.


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## GunsOfNavarone (May 9, 2020)

HarryJM said:


> Math, beyond simple addition, division, multiplication, has always been a challenge for me as I generally like to learn new things that I can use and trig was not something that I found a use for until I started my metal working hobby and educating myself via this forum and YouTube.
> 
> The below Joe Pieczynski video for setting a lathe compound to precision angles is a good example of a lathe trig application and yes I had to watch it several times before it started to make senses.


I SOOO didn't think I'd would ever need this stuff in school (not that I would have retained it this long) It's like you should live your life backwards, I'm ready and willing to learn now what I scoffed at in my youth. Its almost fascinating to me now?


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## HarryJM (May 9, 2020)

GunsOfNavarone said:


> Its almost fascinating to me now?


That's where I'm at when every I come across a trig solution for a metal working procedure/etc.


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## middle.road (May 9, 2020)

I took math all four years in high school, but when I got to trig & calc senior year there were only (5) of us and we got stuck in with an 'advanced' class and the teacher did not have any time for us 'slow learners'. He spent all his time with the advanced students and none with us.
Then one fine day he shot his mouth off stating that we were indeed 'slow learners' and that we should have already taken the T&C classes Junior year and that he didn't appreciate wasting his time teaching basic math.
That did it for another student and myself and we gathered our books, left the class and headed down to the counselors office to drop the class.
The other three dropped the class the same day and then the 'advanced' class no longer had the needed (12) bodies in the class required to keep it scheduled. 

Fast forward two years ('79) and I get tasked with "trig'ing" out drawings for the CNC Programmer to use to code parts on our large horizontal mill.
I was screwed.
A buddy who was a QC engineer got permission from his boss to teach me trig a couple hours a day for a week.
Thank you Jim! Saved my arse. Illinois Tool Works (ITW) had a booklet with the same charts above in #13.
Bought a Toshiba electronic calculator, thank goodness they were available.

A couple of years after that Sharp came out with their EL-5xxx series of calculators with available _cassette interface_.
Bought some TRS-80 math programs on cassette at Radio Shack and was able to adapt and hack them onto the Sharp.
Used it for years.

Nowadays I go the CAD route. I have LibreCAD on the Linux laptop out in the shop for 'quickie' stuff.


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## Suzuki4evr (May 9, 2020)

I only like it when I understand it and works for me


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## GunsOfNavarone (May 9, 2020)

Suzuki4evr said:


> I only like it when I understand it and works for me


And that's fair. I think that is my problem now. It wasn't easy, didn't need it THEN and now I don't have a classroom with a teacher to teach me and answer my questions. Is it fair to say it seems even harder now? Maybe it the lack of that structure making it so challenging..


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## Suzuki4evr (May 9, 2020)

I past by the skin of my behind in school, but got 79% in college, don't know how I did that though. As for teachers you need,you will get it right here at H-M (please don't ask me  ) and YouTube of course.


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## Winegrower (May 9, 2020)

I’ve had a whole lot of years of math, so trig and algebra are natural and I use them in the shop all the time.   I observe that the basic problem is that teaching math is done in a way that makes most people hate it.   The problems they give you are uninteresting, meaningless and irrelevant.   I wish I could get up the energy to teach a first year calculus class and make it extremely understandable and useful.   We might have to review some basic stuff, but I believe anybody interested in machine tools has all the brainpower needed to actually enjoy this stuff.   Yes?  No?


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## Lo-Fi (May 9, 2020)

Winegrower said:


> I’ve had a whole lot of years of math, so trig and algebra are natural and I use them in the shop all the time.   I observe that the basic problem is that teaching math is done in a way that makes most people hate it.   The problems they give you are uninteresting, meaningless and irrelevant.   I wish I could get up the energy to teach a first year calculus class and make it extremely understandable and useful.   We might have to review some basic stuff, but I believe anybody interested in machine tools has all the brainpower needed to actually enjoy this stuff.   Yes?  No?



This. So much this. I have exactly the same experience. If something like Khan Academy was available when I was at school, I think I'd have had a better time. 

That being said, I'm not entirely sure advanced maths is appropriate to teach in mandatory mainstream education where tuition is freely available online. An overview such that you know what it is and does should you need to use it in your life or career might be much more effective, and time in class better spent explaining in detail the mathematics behind, say, credit/savings interest that's unilaterally useful in life. At the end of the day, the rigid educational model is a prehistoric anachronism in the modern world and needs looking at differently. Everyone is different, and it fails the majority of students as it is.


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## mickri (May 9, 2020)

I found math to be rather boring.  Memorize a bunch of formulas and just plug in the known numbers to get the unknown number.  Never went past algebra II.  The high school counselors didn't like that.  You should have heard them scream when I wanted to take home ecc.  I mean that's where the girls were.  They never did let me take that class.  Barely let me take advanced auto which I have used all of my life.  They wanted me to take worthless liberal arts type classes like yearbook, journalism, poetry, etc.

Back before there were gps' I dabbled in spherical trig to help learn celestial navigation for boat navigation.  Still have the sextant on the boat and use it occasionally.  When I was out cruising on my sailboat I researched how the old time navigators from the 1600's, 1700's and 1800's solved the navigational triangle so they knew where they were.  Created some worksheets to help plug in the numbers in the right places.

Math comes easy for me.  What can I say.


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## Suzuki4evr (May 9, 2020)

mickri said:


> Math comes easy for me. What can I say.


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## Suzuki4evr (May 9, 2020)

Just kidding mickri,you are one of the lucky ones


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## derfatdutchman (May 9, 2020)

I was never a math wiz, but as as I have a calculator and a Machinery's Handbook I can muddle through.


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## dirty tools (May 9, 2020)

I had a brain tumor operation in 1990 and ever sense I have Extream problems wi math (very difficult to just add and subtract)


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## HarryJM (May 10, 2020)

I stumbled across the carpenter's 3-4-5 rule to make square corners when I was building a big 3 tiered raised bed out of 6x6 lumber and although not metal related it is another example of a practical example of math for everyday use.


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## Janderso (May 10, 2020)

I discovered the app, Trig Solver. Simple and easy.


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## Janderso (May 10, 2020)

Winegrower said:


> I’ve had a whole lot of years of math, so trig and algebra are natural and I use them in the shop all the time.   I observe that the basic problem is that teaching math is done in a way that makes most people hate it.   The problems they give you are uninteresting, meaningless and irrelevant.   I wish I could get up the energy to teach a first year calculus class and make it extremely understandable and useful.   We might have to review some basic stuff, but I believe anybody interested in machine tools has all the brainpower needed to actually enjoy this stuff.   Yes?  No?


I don’t even know what kalkulus is .
I think anyone who has had a teacher that made the subject interesting and fun is very fortunate.
In my experience, good teachers were far and few.


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## Bob Korves (May 10, 2020)

Tozguy said:


> Back in 1963 at technology school we were shown how to use a slide rule and math tables. To this day I look up the values of trig functions in the same book of math tables.  No one dreamed about using a small portable wireless phone to replace all the books and professors we had at the time.


I had similar experiences to Tozguy, but in 1966.  I caught on to trig easily, had the formulas in my head, and could get answers in short order, using the charts in the back of the textbook, same as Tozguy.  Now I use online sites for the tables, and I still remember the basic geometries.  I also still have my high school textbook for the basic tables and formulas should they be needed.  I find trig to be a useful tool for life ,not an obscure thing to forget about after high school...


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## Suzuki4evr (May 10, 2020)

HarryJM said:


> I stumbled across the carpenter's 3-4-5 rule to make square corners when I was building a big 3 tiered raised bed out of 6x6 lumber and although not metal related it is another example of a practical example of math for everyday use.


I have also used this quite a bit since I was taught how to use it by my last boss in 09'. I just showed someone a while back how to use it and felt good about it. NEVER  in my life I thought I could teach someone about a math matter.


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## DavidR8 (May 10, 2020)

My dad left was in an orphanage aka ‘boys home’ in England till 1936 when he was 16 at which point he was shipped to Canada as a “home child”. As a result he didn’t get any formal schooling past grade 6. 

After the war taught himself math, sometimes by candlelight while living in a tent so he could be a surveyor to help build roads in Alberta. He eventually retired with the title of “Resident Engineer”. 

These are the cover pages of one of his trig books. They saved me in high school. He also didn’t allow me to have a calculator. Physics 12 was brutal. 












Sent from my iPhone using Tapatalk


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## Aukai (May 10, 2020)

This is my math....


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## westerner (May 10, 2020)

Bob Korves said:


> I find trig to be a useful tool for life ,not an obscure thing to forget about after high school...


I suppose it all depends on the life one leads after high school.....


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## Janderso (May 11, 2020)

westerner said:


> I suppose it all depends on the life one leads after high school.....


True,
I haven't needed to figure out a trig. problem in 40 years.


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## Winegrower (May 11, 2020)

DavidR8’s post reminded me of my own father...he only finished high school, and somehow became a machinist at Hickham field in Hawaii and eventually a toolmaker.    I remember him teaching me logarithms using tables, and how to extract square roots by hand when I was in 6th grade.   I suppose all good machinists in those days needed to know some of these things, but I am impressed with his ability to use and explain them.   They say you don’t understand something until you try to teach it to another.


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## Aukai (May 11, 2020)

It's strange, my dad was a Navy pilot, had a few degrees, one being in math. He was stationed in Washington DC at the bureau of naval weapons designing torpedoes, and underwater mines, and I struggle immensely with math. I feel unbright now, but I made it this far, Macgyvering my way along.


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## Janderso (May 11, 2020)

Aukai,
It's interesting how we evolve from our parents. My dad was brilliant in math. He ended up in business as a Ford dealer but he never forgot anything when it came to math. He would help my brother and I (my brother is very good in math)  and I would watch in awe as he rattled off formulas and equations from his High School days.
On the other hand, he didn't know which way to turn the screw driver. he would break the lawn mower and I would fix it at a young age.
He would get a kick out of his mechanic son.


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## Aukai (May 11, 2020)

Your right LOL, my stepson has a PhD in mechanical engineering, not sure he could change a head light.


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## Janderso (May 11, 2020)

We all have our different strengths.
Example......


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