I've been helping/tutoring/coaching a friend through some college trig the last couple of weeks. I told him I'd be all over it without a thought. The first thing he came upon was angles in radians. Who the freak uses radians? I had troubles with them 32 years ago and guess I still do. Once I finally got it figured out again, he's passed that part now.
Something else I completely forgot about and screwed him on is the quadrants. Surveying and physics quadrants run oposite of regular math quadrants. In math, angle 0 points due East. We all know we use 0 is due North. Same in physics. I remember now in high school taking trig and physics in the same semester and was always getting them confused.
Oh well.
E.
Excel uses radians for trig functions so you have to convert back and forth.
2pi radians = 360°, pretty simple really.
check out the calculator next time you use it. most have a deg>rad converter
One radian is the angle where the arc equals the radius, which turns out to be 57+ degrees.
That fact is worth remembering in order to mentally check you did the right steps in converting using pi.
There are exactly 2*PI radians in 360 degrees, so the math works out nicely when using radians.
My high school trig teacher taught us to remember the number 1745.
Because one degree = 0.01745 radians and one radian = 57 deg 17'45".
Also, radians can convert easily into arc length, i.e. the angle in radians X the radius equals the ARC length, i.e.
1 degree = 0.01745 radians; so for a 100' radius; the arc length on one degree is 1.745 feet.
1 Radian = 180°/pi
Being a Luddite on a Sunday afternoon..........
How do radians "feed the cattle" ?
TNAI
Radians are dimensionless. For geodetic calculations, it is typical procedure to do computations with angular measurements in radians.
PI to 9845 places
3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 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PS I tried plugging this value into my handy dandy keyboard calculator using CTRL V and it crashed it 😀
You all are missing my point.
Who uses them for real?
Handy to compute and arc-length - ok, I'll give you that.
Next time one of you guys or gals has nothing better to do, take one of your plats wtih lots of bearings in DMS and convert the entire thing to be in radians. Take it to the county to file or give it to a knowledgeable client and see how that goes over. 🙂
E.
> You all are missing my point.
Pretty bold statement there
> Who uses them for real?
We all do..
> Handy to compute and arc-length - ok, I'll give you that.
Adding and subtracting angles also
> Next time one of you guys or gals has nothing better to do, take one of your plats wtih lots of bearings in DMS and convert the entire thing to be in radians.
I dont think that would work very well Eric.
I remeber it like this.
The radius of a one degree curve is 5729.578
one radian is 57.29578 degrees.
Simple huh.
Or..
2PI/360 = 1° (decimal) /60 = 1' (decimal) /60 = 1" (decimal)
Heck here all this time I thought the 'rad' button on my calculator was reservered for only the 'cool' people.
I never used it because I am not.
RAD
adjective
Definition:
excellent: very good, desirable, admirable, or fashionable ( slang )
a totally rad idea
Good one, John...
I guess that is why I get is so much trouble...with that SIN key and all...
DDSM
yeah I thought my 'tan' key was broken.
I'm white as a ghost.
Hahaha
You two guys...sheesh LOL
Here is my main point. It's easier for me visualize degrees.
Quick: what does 45 degrees look like? Sure same as 1/4(pi) radians.
Quick: what does N 45 degrees W look like? Sure same as 3/4(pi) radians.
Ask a lay person who knows how to deal with a compass and have them compare both.
Eric
You are mixing up the measure of an angle and a direction of a line.
ok Paul
135 degrees is still easier to envision than 3/4(pi) radians.
In any event I did finally get a grip on it all again and got my buddy passed with a middle-B.
So I'm going to drop it now.
E.
