/sci/ - Science & Math

[Anonymous No.5145724]

Okay, so fall freshman here. I consider myself alright at math, but have never been that great at it like some of you guys. I placed into Precalc 2 which is the second highest I could get into, and I was wondering if you guys can help me conceptualize some things.

What is the point of trigonometric functions? I understand that using sin, cos, etc lets you determine the dimensions of a right triangle if its applicable. But my textbook keeps saying that they have huge practical uses, and gives long equations as examples but doesn't explain how the trigonometric functions actually play a part in it. Can you guys explain to me how trigonometry is used in everyday mathematics? Is there some concept I'm not getting?

Secondly, can I somehow put the exact coordinates of the unit circle into my graphing calculator (i.e. not decimal points put in terms of pi)? I always end of mixing them up on tests a few times.

[Anonymous No.5145737]

Well, in math, you won't go any further without trig, so that's how its important lol.

Coordinates, as in [(3)^2]/2 , 1/2? Those are exact, you can't use pi for the coordinates

[Anonymous No.5145739]

Later in the book you'll use all of the trig identities, double angle theorem, half angle, herons formula, law of cosines, etc etc to solve mostly real life problems of airplane heading and whatnot. It's very important to understand the trig table first.

[Anonymous No.5145740]

>>5145724
>What is the point of trigonometric functions?
Trig functions are highly practical. I'm sure you did those geometric things in high school where it gave you an angle and a height then asked you how far away some object was. On a more advanced note, trig functions are useful in engineering for things like vibration analyis or dynamic systems, and learning about suspensions.

Secondonly, just do <span class="math">\frac{/pi}{x}[/spoiler] for your normal exact values.

[Anonymous No.5145743]

>>5145737

Sorry, I mixed that up. I meant not as a decimal.

And, well, how would a mathematician use trig then?

[Anonymous No.5145745]

EE here.
>What is the point of trigonometric functions?
What is the point of multiplication?
Depends on the application.
For me sin and cos are orthogonal in Hilbert space. That allows other functions to be represented as integrals of those 2 (integral transforms). This is how image compression works (on 1st order scale).

[Anonymous No.5145763]

>>5145724
An easy-to-understand application of trigonometric functions is the description of waves, oszillations and periodic activity in general.

[Anonymous No.5145769]

>>5145763
That. And also the fact that they always pop up in solutions to differential equations, so you can't really avoid them.

[Anonymous No.5145778]

>>5145724
>(i.e. not decimal points put in terms of pi)?
Use the better circle constant.

[Anonymous No.5145797]

>>5145724
>they have huge practical purposes

Programmer here, yes they do have practical purposes.

Ok, so let's say you have a Banshee on Starcraft and you want to move him to a different part of your screen. So you click where you want him to go. What angle does he turn? What direction does he go? It's all trig.

So you have the x,y coords of the mouse and you have the x,y coords of the Banshee. What trig function uses the sides of a triangle that represent x and y? That's right, Tan.

So Tan is y/x, so for simplicity sake, let's just say the Banshee is at point 0,0. That way, we can just use the x and y coord of the mouse. So first we find the angle between the Banshee and the mouse, so we take y/x and run the inverse Tan on it,

angle from Banshee to mouse = arctan(y/x)

So now we have the angle, which is great. Now when the Banshee moves, every frame he moves sin(angle) on the y-axis and cos(angle) on the x-axis. Of course, on the unit circle that could only go as high as 1, so it is necessary to multiply the number you get by the speed of the Banshee. In summary:

angle = arctan(mouseY / moueseX)
Banshee Y value increases by sin(angle)*speed
Banshee X value increases by cos(angle)*speed

Note: If the Banshee's x,y isn't 0,0 then just mouseX-bansheeX, mouseY-bansheeY to get the right relative mouse coords.

[Anonymous No.5145838]

Without trig functions how would we Fourier series??!! Well I guess technically without e but whatever lol.

[Anonymous No.5145853]

Mechanics and kinematics in physics use a lot of trigonometry, so it has tons of practical uses in architecture and engineering.

[Anonymous No.5145879]

>>5145778
<3