Why Are 30, 45 And 60 Degrees Significant?

I took trigonometry in high school, and I still find it a fascinating topic. I never pursued the topic any further beyond that (and I am probably going to shock many of the more educated among you with my lack of knowledge on the topic), but one thing they taught me still stands out.

We were taught how to get the exact values of the Sine of 30°, 45° and 60°. I will skip the details. But as many of you already know, that involves constructing a square and an equilateral triangle and using the Pythagorean Theorem. But this is what I found interesting: We were told to remember the values, because the Sine of 30°, 45° and 60° come up often in science.

How do they come up often in science?

As I said, I didn't have any trig beyond high school. So what you post will probably be just beyond that.

As yes, I do think they often dumb down our educational system. But that is another debate altogether.

Thank you in advance to all who reply

:daisy: :alien: :daisy:

 

mostly if you build pretty much anything you will use Pythagoreans rule


flooring guys specially...architects...farners.....it is out there everywhere

 

How could one go about drawing a triangle with 3 right angles? Would using a sphere as your plane help?

 

I actually think I may have seen exactly what you are talking about. But I don't recall if it was on tv or on the internet, so finding it might be hard (sorry).

Actually, as I understand it, we may be living on a sphere. Or space may be curved, in any event.

 

Here's a vid where the triangle made of three right angles on a sphere is explained (it starts at about 28:00) He brings up the geometry of the universe around 34:00 as well. https://www.youtube.com/watch?v=sbsGYRArH_w

 

i really don't remember much trigonometry at this point, but it just seems kind of intuitive that those angles would be significant. they're 1/3, 1/2, and the other 1/3 of a right angle. they come up in normal life fairly often, so why not in science?

 

Pythagoras

 

Trig was part of grade 10 math I am pretty sure. I am not a huge math fan but I remember trig being kind of cool.

My boyfriend occasionally uses trig when making electronic music. Don't ask me what for I just know I've seen him scribbling sin waves and things on scrap paper while working on new songs before.

 

quite sure its used pretty extensively in electrical engineering.

 

I don't really 'know' trig when making music but I do know that it can be used to shorten or lengthen sound waves. This tends to give the music dynamic qualities so a certain sound may have a more abrupt cut-off in terms of it's waves, like what we hear with a note that has a really sharp, brief sound, in musical terms is a stacatto, as where other times waves will have a more oscillating wave and waiver more in the music, in musical terms a tremolo, or it may have a flatter wave and ring out with the same tone for awhile , in music terms a sustain.

You can slightly alter the waves too, so one stacatto sound may be a sharply rising sound, as where another can be a sharply descending sound and all kinds of fascinating stuff in between.

 

I assume quite frequently since they are respectively 1/3, 1/2 , 2/3 of 90° or a right angle.

 

highschool trig is baby stuff. here's some of the stuff I was talking about, electrical engineering is a field where trigonometry finds much application, where the relative phase of signals is concerned especially.
https://en.wikipedia.org/wiki/Quadrature_amplitude_modulation

@ GB: what you were saying above: isn't that referred to as "envelope" ?

 

What I'm describing would probably be better categorized as frequency and amplitude, although I think it could be considered "envelopes" as well. One reason to make this distinction however, is that with a digital music workstation like FLstudio for instance, there are separate functionalities which are explicitly called envelopes in the program, that you can overlay on top of the frequencies and amplitudes.

These envelopes help in like fading a song out at the end or in the builds of electronic music, like that climaxing "Swoosh" sound on synths that is often used in EDM before the beat drops again.

 

since a “full circle“ contains 2π radians (a radian is defined as the central angle θ when the arc length s is equal to the radius of the circle .. think of it as a slice of a circle where the arc length is equal to the circle’s radius) then 90° is π/2 rad.

30°, 45°,and 60° are thus π/6, π/4, and π/3 rads respectively and are “easy angles“.

why it is like this idk tbh except that mathematically it works. as for the significance of certain angles, I would imagine it would depend on the applications, of which there are many “phase shifts“ in electrical signals are just one.

if you take the function for the area of a circle A( r) = πr2 and differentiate; the first derivative would d/dr = 2πr, and if you differentiate again the second derivative would be d(d/dr) = A``( r) = 2π

^at this point you’ve lost your independent variable and what you have is no longer a function anymore, rather an expression that is equal to the number of radians in a circle.

How they figured this out without calculus in the first place ... well idk but sometimes math is kinda “circular“ .. heh


I was looking for some old interesting post buried somewhere, this wasn’t it but i had to drop by to say this ... oh yea .. and stop inserting the "registered trademark symbol" for (r) i.e ( r) .. that's very annoying (i had to put an extra space to get it to actually show).

 

"You can build anything with a rule, a set square, a tape measure and a piece of chalk". Ain't that what the oldies say? Shut up, ya old bastard! Motherfucker needs a 360° set bevel. Ain't building nothin' without one!

 

I just use my calibrated eyeball...

 

Nobody needs to tell me something is something of a degree. If I wanna see what degree something is, I look at it.