How do you solve cos(x) = 2x?

Answer 1

x=0.4501836... (in radians)

Answer 2

1 way.... Guess. Then continue guessing in small increments... It's going to be between 0 and 1/2 and likely towards the higher end of 1/2.

a second way is to graph y=cos(x) and y=2x and find where they intersect.

I think the first method is "easiest" if brute force. especially if you use something like Excel. You can put your X values in column A, then for column B, use (cos (A value)-2*(A value)) and find where the value is zero. These are only approximations though.

Answer 3

The only way it could be done as far as I can see is reverse calculation, Try this:

x=1
hcnt=1
Lbl1:
hcnt=hcnt/2
if int(cos(x)*100000)=int(2*x*100000) then goto lbl2
if cos(x)>2x then x=x-1: goto lbl1
if cos(x)<2x then x=x+1: goto lbl1
lbl2:
End

Answer 4

There NO algebraic way to solve it
You must do it numerically
Any way if x>0,5 or x<-0,5 there is no solution
So let´s study the interval -0.5<=x<=0.5
Take the function
y=cosx-2x
at x=-0.5 y(-0.5)= 1.8776
at x= 0.5 y(0.5)= -0.1224
y´(x)= -sinx-2 always negative
So the function is decreasing and starts positive and ends negative so there is only one root which you must aproximate numerically
As x=0 y>0
Atx=0.4 y>0
at x=0.45 y(0.45) =0.0004 so x=0.45 is a very good value

Answer 5

I'm not sure you can really solve it neatly. Experience tells my the answer is approximately 1/2 though.

Answer 6

I can't think of any identity you would use for that. There isn't a trigonomic pattern for 2, either. I would divide by x and get cos=2.

Answer 7

I'm not sure...I starred this question to see any valid answers