Print

Please login or register.
1 Hour 1 Day 1 Week 1 Month Forever
Login with username, password and session length

[ILikePie]

Code: [Select]

cos x = sin (x - 40)
cos x = cos (90 - (x - 40))
cos x = cos (130 - x)
cos x = cos x*cos 130 + sin x*sin 130
cos x - cos x*cos 130 = sin x*sin 130
cos x*(1 - cos 130) = sin x*sin 130
cos x = (sin x*sin 130) / (1 - cos 130)
cos x = (sin x*cos (90-130)) / (1 - cos 130)
cos x = (sin x*cos (-40)) / (1 - cos 130)
cos x = (sin x*cos 40) / (1 - cos 130)
Now what?

[Christes]

Is your goal to solve for x?

If so, then I'd suggest dividing sin(x) over to get tan(x) = ...  and applying arctan.  Remember that there will be infinitely many solutions, and that arctan's range is (-pi/2,pi/2)

[ILikePie]

That works, thanks.

[Virex]

Code: [Select]

cos x = sin (x - 40)
cos x = cos (90 - (x - 40))
cos x = cos (130 - x)
cos x = cos x*cos 130 + sin x*sin 130
cos x - cos x*cos 130 = sin x*sin 130
cos x*(1 - cos 130) = sin x*sin 130
cos x = (sin x*sin 130) / (1 - cos 130)
cos x = (sin x*cos (90-130)) / (1 - cos 130)
cos x = (sin x*cos (-40)) / (1 - cos 130)
cos x = (sin x*cos 40) / (1 - cos 130)
Now what?

You're doing it the difficult way. After line 3 you've got:

Code: [Select]

cos x = cos (130 - x), and both sides are cosines, so we can equate the arguments of the cosine, using cos(x) = cos(360-x)
x = (130 - x)mod(360) or  x = (360 - (130 - x))mod(360)
Using that you ought to be able to find x.

[Darvi]

Wait, what? Couldn't he just've done

cos(x)=cos(130-x)      l arccos
<=>x=130-x (+k360)  l +x
<=>2x=130 (+k360)   l :2
<=>x=65 (+k180)

?

Edit: ah wait. Whatever.


cos(x)=cos(130-x)
<=>x=130-x (+k360)    or x=x-130(+k360)
<=>2x=130 (+k360)     or 0=-130(+k360) (impossible)
<=>x=65 (+k180)

Still true.

Edit: f*cking radiants

[Virex]

He's probably working in degrees. Plus, as I pointed out, you'll get 2 sets of intercepts, while your method only finds one. You caught that one

[Darvi]

Yeah, degrees, right. F*cking radiants <_<

[ILikePie]

I can get of the cosines if I have them on both sides?

[Virex]

Yeah as long as you remember you'll get 2 solutions.

[malimbar04]

Yeah, degrees, right. F*cking radiants <_<

It wouldn't be so bad if degrees were never invented. Seriously, who said "lets divide a circle into some arbitrary 360 pieces". They didn't no jack about circles.

[MonkeyHead]

Yeah, degrees, right. F*cking radiants <_<

It wouldn't be so bad if degrees were never invented. Seriously, who said "lets divide a circle into some arbitrary 360 pieces". They didn't no jack about circles.

Babylonians, approx 3000 BC, based on observation that it took 360 days until Earth returned to same point in orbit (as far as they could tell), which they assumed was circular (not a bad postulation). Thier fault.

[ZetaX]

That's not so clear, see http://en.wikipedia.org/wiki/Degree_%28angle%29#History .

[MonkeyHead]

Heh yea, nothing is ever simple.

[malimbar04]

At least it's better than the explanation for Fahrenheit. Every explanation I've heard crazy.

[Virex]

You mean that using half the circumference of a circle makes more sense? Anyway, you can always divide the circle in 400 parts if you like that better.