is this legal?

(mathematically)

if cos²(u) + sin²(u) = 1, then does

cos²(2t) + sin²(2t) = 1?

because technically those are double angle formulas (where cos²(2t) = [cos(2t)]².

and if we let u = 2t, then cos²(2t) + sin²(2t) = 1 -> cos²(u) + sin²(u) = 1. but then we cant substitute 2t back in for u since its just a 1 now and nowhere to plug u into.

No it's not legal, you're gonna get locked up for 25-life. WHAT YOU HAVE DONE HERE IS A FUCKING FELONY, A MOCKERY OF ALL THAT IS SACRED AND GOOD!!!

relax man. im not quite here yet.

 Spoiler

relax man. im not quite here yet.

 Spoiler

Is that the same black hole our tax dollars go into?

relax man. im not quite here yet.

 Spoiler

NOOOOOOOOOOOOOOOOOOOOO

why'd ya have to divide by zero?

Is that the same black hole our tax dollars go into?

secretary of US treasury mustve divided by zero.

If t is a variable and not a function, then yes that's legal.
If t is a function, I'm not 100% sure but I think it's also legal... not sure.

secretary of US treasury mustve divided by zero.

They shred cash and stuff lamps with it, what did you expect?

If t is a variable and not a function, then yes that's legal.
If t is a function, I'm not 100% sure but I think it's also legal... not sure.

the whole problem is (vector) integrating.

i simplified the integral to look like:

inte[sqrt(144(cos²(2t) + sin²(2t)) + 25)]dt

if i did cos²(2t) + sin²(2t) = 1, then it'd look like

inte[sqrt(144(1) + 25)]dt
=inte[sqrt(169)]dt
=inte[13]dt = 13t

the answer and final stepped looked to easy and simple so i wondered if doing that trig thing was legal lol. its suspicious when complicated math problems come out to have simple answers.

No but this is:

 Spoiler

All jokes aside, yeah, that's valid maths.

cos²(u) + sin²(u) = 1
Holds valid, as long as the arguments of the trigonometric functions, u, are the same.
So, since u = 2t, it would be true for
cos²(2t) + sin²(2t) = 1
But not true for
cos²(2t) + sin²(3t) = 1
since 2t is not equal 3t (unless t = 0).

And yes, I do believe that is the correct solution for the integral.

inte[sqrt(144(cos²(2t) + sin²(2t)) + 25)]dt

What you are doing is u substitution. in order for your theory to be viable, you would have to do the following:

u= 2t --> du = 2 dt

so technically the answer you have is wrong since you did not compensate for the 2dt...

But all the other math workings i can't do, since i'm not in a high level calculus class =P

i.e. no clue how to do this... but you can do the u thingy if you compensate for the dt part...

You don't have to do u substitution. cos²(2t) + sin²(2t) = 1.

inte[sqrt(144(cos²(2t) + sin²(2t)) + 25)]dt

What you are doing is u substitution. in order for your theory to be viable, you would have to do the following:

u= 2t --> du = 2 dt

so technically the answer you have is wrong since you did not compensate for the 2dt...

u was just a random variable. i didnt do u substitution, it was trig substitution/trig identity.

13t + c



You'd need a specific solution to know what c is.

I snap. Your getting death row now D:>

QUICK! TO THE ESCAPE POD! LAWYER!

13t + c



You'd need a specific solution to know what c is.

it was a definite integral 2u2

thanks to people who answered. people who didnt can go get divided by zero now.

uhh sorry I don't do Specialist Math :f6:

Wow... that looks kinda confusing, shame I only do Methods 3/4

You know about that 1 over there? I'm pretty sure that means the t's have canceled each other like matter on anti-matter. And you're not doing anything illegal as far as I can tell.