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Tutorial on Trig.....Not

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Kenny G

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A short while back one of the members was asking about a Trigonometry tutorial. It got me to thinking (not always a good thing) and I decided to make up a kind of outline that shows my logic when it comes to solving right triangle problems. This is not a tutorial by any means and I am not a mathematician either. I tried to include every possibility for solving a right triangle that I can think of using some very basic trig and algebra.



I have broken it down into 3 basic functions the Pythagorean theory, Tangent function, cosine and sine functions. I’ve attached a PDF and a DXF file of my process. I used a basic 3,4,5 right triangle y=3, x=4, and r=5. I am in no way suggesting this is the only way to to approach this and encourage others to show their methods it is kind of a fun mental exercise. Please feel free to check my formulas, I did but I am not perfect and you may find some sort of error.
 

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GunsOfNavarone

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#2
I think that may have been me....and I will be all ove this. Thank you for the work you put in!
 

GunsOfNavarone

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The first one completely loses me, 2nd one my ipad and android tablets can't open. Where does SOHCAHTOA come in to play here? Or is that about 30 lessons prior?
 

ddickey

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#4
It's what you use to figure out an unkown length or angle of a right triangle. one of the three. SOH,CAH or TOA.
 

RJSakowski

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A short while back one of the members was asking about a Trigonometry tutorial. It got me to thinking (not always a good thing) and I decided to make up a kind of outline that shows my logic when it comes to solving right triangle problems. This is not a tutorial by any means and I am not a mathematician either. I tried to include every possibility for solving a right triangle that I can think of using some very basic trig and algebra.



I have broken it down into 3 basic functions the Pythagorean theory, Tangent function, cosine and sine functions. I’ve attached a PDF and a DXF file of my process. I used a basic 3,4,5 right triangle y=3, x=4, and r=5. I am in no way suggesting this is the only way to to approach this and encourage others to show their methods it is kind of a fun mental exercise. Please feel free to check my formulas, I did but I am not perfect and you may find some sort of error.
Your expressions for determining the angles do not look correct (at least not anything that I have ever seen).

Using your terminology, α = arctan(y/x), α = arccos(x/r), and ß = arcsin(x/r). They can also be written as α = tan-1(y/x), α = cos-1 (x/r), and ß = sin-1 (x/r).

I couldn't insert the superscript -1 but you get the idea.
 

P. Waller

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The first one completely loses me, 2nd one my ipad and android tablets can't open. Where does SOHCAHTOA come in to play here? Or is that about 30 lessons prior?
It is a mnemonic method to help people remember the basic trig functions, this is part of Highschool trig classes.
You didn't pay attention did you (-:
 

Kenny G

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Kenny G

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you're absolutely right it should have been tan^-1,cos^-1etc example a=tan^-1(x/y). I was trying to reflect back on the other formulas and should have written it a=tan^-1(tana) where tana=y/x. said I may have made some errors just deleted it in the pdf and dxf and also corrected Pythagoras. Thanks all
 
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MrWhoopee

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#10
I took a lot of math in high-school and JC. The only trig I remember (or have needed) was SOHCAHTOA. Never came up against a triangle it couldn't solve.
 

higgite

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#11
Not to be picky, but... yeah, well, okay... to be picky, it's Pythagorean Theorem, not theory. There is a difference. If we're gonna teach it, let's teach it right. ;)

Tom
 

P. Waller

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#12
Make it far more simple, give home machinists the trig calculations that are often used in the machine shop business. There are a limited number of functions that are relevant and will be useful to most.

Depth of a 60 Deg. v-thread to the theoretical sharp V for instance, .866 of the lead, you can not achieve this because no tool has a sharp corner.
However the math looks like this.


Sine of 60 Degrees = .866 per unit always, regardless of the unit used.
A 3/8-16 thread has a .0625" lead
.0625" X .866" = .0541". This yields a minor diameter of .267" which is well below the published diameter of .312" for a hole to be tapped, threads are not sharp vee forms, they have either a flat or radius at the creast or root.

You have a smart phone I suspect, it may well have a calculator that has Trig functions included. The phone may call it a scientific calculator.

If you need to calculate a taper in degrees and arrive at a start and finish diameter in units over a known length of the same units.

The Tangent of the angle will provide the answer.
The tangent of 3 degrees is .0524 per unit. If lathe work it will be an angle of 6 degrees included.
If you want to produce a 3 degree taper over a distance of 1 unit the finished end will be .0524 units smaller per unit, this is way simple to figure out.
 

9t8z28

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#13
The best way to remember SOHCAHTOA is to remember this saying,
Some Old Hippy Caught Another Hippy Tripping On Acid
It works because its funny to say in your head!
The first one completely loses me, 2nd one my ipad and android tablets can't open. Where does SOHCAHTOA come in to play here? Or is that about 30 lessons prior?
 
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