Trig functions & Private Pilot Test

Gosh. It's scary to see all you engineer/science freaks geek out over your reverse Polish notation machines. (Yes, I know what you mean by RPN!) Brings back bad memories from my childhood. (My older brother was a physics major.)
Guess what? We still teach it in 2nd semester computer science and in compiler theory. It's how many programming languages are implemented.
 
Guess what? We still teach it in 2nd semester computer science and in compiler theory. It's how many programming languages are implemented.

I'm sure. I'm not questioning the utility. I'm just poking fun.
 
I borrowed a friend's HP48gx with the survey pack when I took the civil PE. It got me through the 4 hour survey test, plus made one of the problems on the 8 hour a gimmie. I didn't have a background in all this civil survey crap.

Now those are fairly useless (except maybe for the exam.) All of the actual work is done in CAD.
 
However....the testing site has the option to allow or disallow any electronic calculator, even if the FAA says it's ok to use. Details in the tiny small print somewhere in the FAR or AIM, I don't remember which.

As for an E6B - PITA. I still have my K&R slide rule Dad bought me when I started engineering school. Never learned to use it. The manual E6B is just another version of a slide rule. There are too many other resources to be limited to the slide rule. Fortunately, most E6B have the instructions for wind calculations printed on them, which is legal for all exams. That's right - if your E6B has the details, they can't disallow it.

On the other hand, the trig/wind problems can be fairly well managed by remembering this:
45 deg is 0.707 (sin or cos)
30 deg sin = 60 deg cos = 0.5
30 deg cos = 60 deg sin = 0.87

Don't remember the triangle picture for sin & cos? NASA has great examples.

An E6B is nothing more than a specialized circular slide rule. East to use, even with one hand (which can be handy in the cockpit in rough air). Now, do I use it when flying? Not likely. Most calculations I need to perform can be done in my head with enough accuracy "for government work".

My engineering slide rule, which I learned how to use, is a Pickett N4-ES double log. Got it when I started college in 1970. Still used it as a trig and log table after buying my first electronic calculator (TI SR-10) in the spring of 1973. Couldn't afford an HP-35 back then. I still use my HP-41CV that I bought back around 1981 or so. It still works and meets my needs, including programs I wrote for it "back in the day". Oh, and I know exactly where that slide rule is and I know how to use it.

Aww, come on, if you can use one to navigate a starship, it should be fine for anything on the written test....

e6b.jpg

Nimoy was a pilot. He knew how to use that thing.
 
An E6B is nothing more than a specialized circular slide rule. East to use, even with one hand (which can be handy in the cockpit in rough air). Now, do I use it when flying? Not likely. Most calculations I need to perform can be done in my head with enough accuracy "for government work".

My engineering slide rule, which I learned how to use, is a Pickett N4-ES double log. Got it when I started college in 1970. Still used it as a trig and log table after buying my first electronic calculator (TI SR-10) in the spring of 1973. Couldn't afford an HP-35 back then. I still use my HP-41CV that I bought back around 1981 or so. It still works and meets my needs, including programs I wrote for it "back in the day". Oh, and I know exactly where that slide rule is and I know how to use it.



Nimoy was a pilot. He knew how to use that thing.

As was Gene Roddenberry, who was actually a airline pilot.
 
To how many decimal places? And, to specifically get back to the test, studying what you need to know for the the test and learning what you should know to fly are not the same thing. 1/cos(bank) is an excellent example of that as you suggest.

To as many decimal places as you have the significant digits of precision to measure the angle of bank and the g-forces. It’s physics. Basic physics at that.

I think you’re reading more into my point than is there. All I’m saying is that for those of us who do know vector math and trig, it would be faster on the written test if those calculators could be used. Not saying anything at all about the usefulness of knowing that the g factor is 1/cos in real life.




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Postfix notation - welcome to the world of HP Calculators!

"Welcome"?? I bought my first HP in 1984, my second (and current one) in 1986. "RPN Calculator" is on my phone for when I'm away from my desk, as is "go41c" on my tablet. But feeling the buttons press is much better than stabbing at a spot on the touchscreen that feels like all other spots on the touchscreen . . ..
 
Oh, the argument clearly has nothing to do with "you must know how to use a slide rule because that's in some way better than using an electronic calculator"...the proctor gave me an ASA CX-2 to use during the test.
 
An E6B is nothing more than a specialized circular slide rule. East to use, even with one hand (which can be handy in the cockpit in rough air). Now, do I use it when flying? Not likely. Most calculations I need to perform can be done in my head with enough accuracy "for government work".

My engineering slide rule, which I learned how to use, is a Pickett N4-ES double log. Got it when I started college in 1970. Still used it as a trig and log table after buying my first electronic calculator (TI SR-10) in the spring of 1973. Couldn't afford an HP-35 back then. I still use my HP-41CV that I bought back around 1981 or so. It still works and meets my needs, including programs I wrote for it "back in the day". Oh, and I know exactly where that slide rule is and I know how to use it.



Nimoy was a pilot. He knew how to use that thing.
Same age. I couldn't afford the SR-10.
 
I gave up on finding a decent RPN calculator for my iphone. A free one at least. But, for the desktop and laptop, Excalibur works great.
 
I gave up on finding a decent RPN calculator for my iphone. A free one at least. But, for the desktop and laptop, Excalibur works great.

I found a great free HP-15C simulator for my iPads. Try here: https://itunes.apple.com/us/app/retro-15c/id583559000?mt=8

I use RealCalc on my Android phone; don't know whether there's an i-thing version. It can be set for RPN as an option.

I used a TI-58 through college, but once I graduated and started my professional career it developed problems. Several of the keys began to double enter, and it kept getting worse and worse. I wanted a professional grade scientific calculator that was programmable and that I could drop into a pocket, and the HP-15C was the perfect answer. That was Oct 1984, and it's still a great answer and still going strong.

I collect old engineering artifacts and have a dozen or so slide rules, all different types, sizes, and constructions. Also have an Addiator. A 6-inch slide rule plus an Addiator makes a great non-electronic scientific calculator. :)
 
Actually the E6B is pretty clever. I still carry one, including a tiny plastic card one I got as a freebie from an Exxon FBO somewhere. You won't have do calculate wind triangles ever again, but the rotary dial still handy for computing TAS, density altitude, ETA for fuel reserve estimation, etc.

Sure, your fancy cockpit GPS can do this kind of thing with their built in apps, but the E6B is quicker for many tasks.
 
I found a great free HP-15C simulator for my iPads. Try here: https://itunes.apple.com/us/app/retro-15c/id583559000?mt=8

I use RealCalc on my Android phone; don't know whether there's an i-thing version. It can be set for RPN as an option.

I used a TI-58 through college, but once I graduated and started my professional career it developed problems. Several of the keys began to double enter, and it kept getting worse and worse. I wanted a professional grade scientific calculator that was programmable and that I could drop into a pocket, and the HP-15C was the perfect answer. That was Oct 1984, and it's still a great answer and still going strong.

I collect old engineering artifacts and have a dozen or so slide rules, all different types, sizes, and constructions. Also have an Addiator. A 6-inch slide rule plus an Addiator makes a great non-electronic scientific calculator. :)

Wow, that is a bit of history there. My engineering career started in 1987 when I entered my univerities BSME program.
 
I actually learned RPN in junior high (middle school) around 1974?, my brother was in engineering school and bought one of the original HP ones, complete with red glowing LEDs. It had a great manual with it and it could run simple programs. It had a lunar landing game you could program in where you "fired" the engine to try to get a soft landing. Good times, lol. When I went to engineering school in 1980 the 15C had come out, so I bought one, it still works. Only a few of us had them and it was a good laugh when someone who didn't know RPN tried to find the equal sign. For most equations that calculator would cut the solution time in half, I'd be on to the next problem while the TI people were trying to figure out which parenthesis they missed.
 
All you need is your basic $2 calculator from walgreens... That's actually what I used. An electronic e6b is nice, too.
 
Oh, the story doesn't end there...The thread will continue on for a while, and eventually a new, nearly identical thread will start.

Ended up chatting with an FAA inspector on this subject. It does appear you are right that the story is not over...
 
Testing center proctor/supervisor here... in our procedures manual it specifically states that only a "basic four function with no memory storage" is allowed. We provide them but an applicant can bring their own I just have to press clear. An electronic E6B is allowed but again I have to clear it. I would be shocked if the procedures of the different sites were any different from that. But training is inconsistent so I'm not surprised people have gotten different (and incorrect) answers, but reading the procedures would get the proctor the correct information. We're not guided by the FAR/AIM, but rather by our ODA procedures manual which is based on FAA 8080.6.


tl;dr - don't be a test proctor.
 
Actually the E6B is pretty clever. I still carry one, including a tiny plastic card one I got as a freebie from an Exxon FBO somewhere. You won't have do calculate wind triangles ever again, but the rotary dial still handy for computing TAS, density altitude, ETA for fuel reserve estimation, etc.

Sure, your fancy cockpit GPS can do this kind of thing with their built in apps, but the E6B is quicker for many tasks.

Yeah, this modern stuff can make you lazy. My PFD displays a wind arrow with H/T components. Pretty accurate after a few minutes of straight and level. Plus IAS, TAS, and GS
 
Testing center proctor/supervisor here... in our procedures manual it specifically states that only a "basic four function with no memory storage" is allowed. We provide them but an applicant can bring their own I just have to press clear. An electronic E6B is allowed but again I have to clear it. I would be shocked if the procedures of the different sites were any different from that. But training is inconsistent so I'm not surprised people have gotten different (and incorrect) answers, but reading the procedures would get the proctor the correct information. We're not guided by the FAR/AIM, but rather by our ODA procedures manual which is based on FAA 8080.6.


tl;dr - don't be a test proctor.
Those were the rules at the one I went to
 
I found a great free HP-15C simulator for my iPads. Try here: https://itunes.apple.com/us/app/retro-15c/id583559000?mt=8

I use RealCalc on my Android phone; don't know whether there's an i-thing version. It can be set for RPN as an option.

I used a TI-58 through college, but once I graduated and started my professional career it developed problems. Several of the keys began to double enter, and it kept getting worse and worse. I wanted a professional grade scientific calculator that was programmable and that I could drop into a pocket, and the HP-15C was the perfect answer. That was Oct 1984, and it's still a great answer and still going strong.

I collect old engineering artifacts and have a dozen or so slide rules, all different types, sizes, and constructions. Also have an Addiator. A 6-inch slide rule plus an Addiator makes a great non-electronic scientific calculator. :)

An Addiator? I haven't seen one of those since junior high. I had one, they were neat.

I had an HP-25C (IIRC) when I worked for the Navy in the late 1970s. Government property, so I had to leave it behind when I left in late 1979. Bought an HP-34C after I went to work for Martin Marietta Denver Aerospace. Great programmable calculator, but it didn't have enough memory, so I got an HP-41CV to replace it. I still use that one today, about 37 years later. I haven't written a program for it in decades, but I still use at least one today, calculates monthly payments for a loan. Feed it the amount borrowed, the interest rate and the number of payments and it spits out the payment. Works great. Every 10 years or so I have to buy a new set of N cells. Now that Radio Shack is gone I'm not sure where I'm going to find those. On-line, probably.

I'll bet I've got something older in my office. An Empire Devices NF-105. If you know what that is, you're an old fart like me. If not, ask and I'll tell you. Suffice to say that when I bought it my wife asked why and I told her it was because I wanted it. Paid almost as much to have it shipped up from San Diego as I paid for it. :D
 
An Addiator? I haven't seen one of those since junior high. I had one, they were neat.

I had an HP-25C (IIRC) when I worked for the Navy in the late 1970s. Government property, so I had to leave it behind when I left in late 1979. Bought an HP-34C after I went to work for Martin Marietta Denver Aerospace. Great programmable calculator, but it didn't have enough memory, so I got an HP-41CV to replace it. I still use that one today, about 37 years later. I haven't written a program for it in decades, but I still use at least one today, calculates monthly payments for a loan. Feed it the amount borrowed, the interest rate and the number of payments and it spits out the payment. Works great. Every 10 years or so I have to buy a new set of N cells. Now that Radio Shack is gone I'm not sure where I'm going to find those. On-line, probably.

I'll bet I've got something older in my office. An Empire Devices NF-105. If you know what that is, you're an old fart like me. If not, ask and I'll tell you. Suffice to say that when I bought it my wife asked why and I told her it was because I wanted it. Paid almost as much to have it shipped up from San Diego as I paid for it. :D


Martin Marietta Denver, huh? I started at Martin Marietta Orlando (Lockheed Martin today) in 1984.

Nope, never heard of an NF-105. Got pics?
 
"Welcome"?? I bought my first HP in 1984,
1974 - HP 35 for something like $300. Agonized for weeks about spending that kind of money.

But, the OP could have solved the problem by just taking a regular slide rule in for the exam. It will do all the trig you ever wanted to do. :)
 
I collect old engineering artifacts and have a dozen or so slide rules, all different types, sizes, and constructions. Also have an Addiator. A 6-inch slide rule plus an Addiator makes a great non-electronic scientific calculator. :)

My granddad just gave me one of his Curta's. Said I was the only one he trusted not to toss it in the trash when he died. Ever use one of those?
 
My granddad just gave me one of his Curta's. Said I was the only one he trusted not to toss it in the trash when he died. Ever use one of those?


I have only seen pictures. Would love to play around with one, though. Pretty cool.
 
Martin Marietta Denver, huh? I started at Martin Marietta Orlando (Lockheed Martin today) in 1984.

Nope, never heard of an NF-105. Got pics?

Denver from October 1979 to October 1983. MX and then "Special Programs". Left the world where a security clearance was necessary and never looked back. :D

NF-105 is a 1950s vintage EMI receiver - 14 kHz to 1 GHz. Band switching is done via changing tuning units. Remove the one for the band you are testing and plug in the next. Interesting piece of history, but I wouldn't want to use one for real today.

Give me an old HP 8566 spectrum analyzer. That's the way an SA should be built - a button for every function. Easy to figure out, unlike all this menu driven junk today. The only downside of the 8566 was it was an instant hernia machine. Sucker is heavy. 112 pounds, IIRC. Could be worse, the old Eaton receiver for 1 to 10 GHz had 4 handles, and we were convinced that that was 1 handle per person to move that beast. There are advantages to modern equipment. :eek:
 
Denver from October 1979 to October 1983. MX and then "Special Programs". Left the world where a security clearance was necessary and never looked back. :D

NF-105 is a 1950s vintage EMI receiver - 14 kHz to 1 GHz. Band switching is done via changing tuning units. Remove the one for the band you are testing and plug in the next. Interesting piece of history, but I wouldn't want to use one for real today.

Give me an old HP 8566 spectrum analyzer. That's the way an SA should be built - a button for every function. Easy to figure out, unlike all this menu driven junk today. The only downside of the 8566 was it was an instant hernia machine. Sucker is heavy. 112 pounds, IIRC. Could be worse, the old Eaton receiver for 1 to 10 GHz had 4 handles, and we were convinced that that was 1 handle per person to move that beast. There are advantages to modern equipment. :eek:


I’m an old servo geek and fell in love with the HP3562. Back when, I loved being able to take closed loop data and convert to open loop with a button push, or even have it draw a root locus plot.

Magic.
 
I wanted a professional grade scientific calculator that was programmable and that I could drop into a pocket, and the HP-15C was the perfect answer. That was Oct 1984, and it's still a great answer and still going strong.
Interesting, as that's roughly the time frame when I bought mine, after my original HP-45 stopped working (I forget what happened to it). Mine, the addressable memory registers started failing around 2014 or so, first 5 and above (so summation arithmetic and mean, SD, etc. became unusable), then register 4, then 3, then by last fall they had all failed. I tried contacting someone who advertises a repair service for old HP calculators online, but he never answered my call or email, so I assume he's out of business. When I realized that HP still makes decent RPN calculators I just ordered a 35s and put the 15c on the shelf in case I ever find someone who knows how to fix it.

My only real complaint about the 35s is that the keystroke sequence to change display precision or format is way more cumbersome than on HP's classic calculators including the 15c. Otherwise it's okay, once you get used to the VERY different key layout.
 
The "unit circle" (radius = 1) does a great job of giving physical meaning to all these trig numbers that are otherwise just numbers
 

1.4plus or minus. We learned the sqrt of the single digits 0-9 in school. Still handy knowledge!

I spent my business career in real estate and the HP-12c was a perfect solution to all our needs. At one point HP discontinued this model and the masses made enough noise that they began to manufacture it again. It is a perfect calculator for the needs of the financial community.

-Skip
 
The calculator spectrum for my career didn't include the abacus but it did start with the slide rule.
 
The calculator spectrum for my career didn't include the abacus but it did start with the slide rule.

I've had basic lessons in both, many moons ago (at about the same time); I can still add & subtract slowly on an abacus, but before I got comfortable with the slide rule, dad brought home a calculator (with lovely green LEDs). But they hit a pinnacle with RPN, and it's all been downhill ever since . . . . .
 
The "unit circle" (radius = 1) does a great job of giving physical meaning to all these trig numbers that are otherwise just numbers
Indeed. I was pleasantly surprised recently to find out that my students were familiar with the concept, so apparently the cosine and sine are still being taught this way in their math classes.

I was beginning to think they only learned SOHCAHTOA. But even with that memory aid, they still have trouble figuring out when to use the different functions.
 
SOHCAHTOA

SOHCAHTOA???

I think I’d need a memory aid to remember that memory aid.

My dad taught me the basics of trig when I was in third grade and wanted to know how high my model rockets were flying. Funny how early lessons stick with one. That was in the days of pulling out the trig tables from a book.




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SOHCAHTOA???

I think I’d need a memory aid to remember that memory aid.

Sine = side Opposite over Hypotenuse
Cosine = side Adjacent over Hypotenuse
Tangent = side Opposite over side Adjacent

And this is from a guy who never heard of it either, who nearly flunked physics 'cause he didn't have trig first and is reaching back 54 years! :)
 
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SOHCAHTOA???

I think I’d need a memory aid to remember that memory aid.

My dad taught me the basics of trig when I was in third grade and wanted to know how high my model rockets were flying. Funny how early lessons stick with one. That was in the days of pulling out the trig tables from a book.




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@dtuuri nailed it. It's supposed to sound like the name of a beautiful Indian maiden I think. Frankly I don't like mnemonics either, but that's how they're learning trig these days. I remember trig tables too, from my high school days. Slide rules as well, though I think I threw my last one out some time ago. Probably should have kept it to do a show-and-tell with my students. Might not go over well anyway though. I can't even interest them in understanding how Vernier scales work, they just don't care. :dunno:
 
Sine = side Opposite over Hypotenuse
Cosine = side Adjacent over Hypotenuse
Tangent = side Opposite over side Adjacent

And this is from a guy who never heard of it either, who nearly flunked physics 'cause he didn't have trig first and is reaching back 54 years! :)

Huh. Seems easier to just remember the above. That’s the way I was taught it, and that’s the way I taught my son. To me, a mnemonic needs to be easy to remember. GUMPS, CIGAR, pretty easy to remember. That whole SOHCOAOAOATOA thing seems hard to remember in and of itself. Seems like once someone has that nailed down, it would be just as easy to remember the basic relationships.

Now, for the master quiz: ILATE? Still remember that after 30+ years, and taught it to my son also. Really helped him out.




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@dtuuri nailed it. It's supposed to sound like the name of a beautiful Indian maiden I think. Frankly I don't like mnemonics either, but that's how they're learning trig these days. I remember trig tables too, from my high school days. Slide rules as well, though I think I threw my last one out some time ago. Probably should have kept it to do a show-and-tell with my students. Might not go over well anyway though. I can't even interest them in understanding how Vernier scales work, they just don't care. :dunno:

Never did learn the slide rule. My dad tried to teach me, but I kept pulling out the calculator and showing him how much easier it was. They did have a large, 10 foot long slide rule in the math classrooms when I took calculus at the local community college. No AP classes at my high school in those days, so I had/got to go to the local CC to get that course in.

Pretty amazing, though, what the engineers could do with a slide rule. Sent man to the moon and designed the SR-71. Impressive.


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