solve cos(x)=x
anyone who dos this step by step is a genius!!
2007-12-06 17:21:33 · 4 answers · asked by MTG G 2 in Science & Mathematics ➔ Mathematics
Newtons method is used for approximations...i want an exact answer...solve it algebraically plz
2007-12-06 17:27:57 · update #1
Gabe u say that the solution is +/- 1 ...mate plz substitute it in the given equation and what u gtis 0 = 1 !!
2007-12-06 17:40:09 · update #2
cos x =x
x = cos inverse x
cos inverse x= cos x
x =x
2007-12-06 17:24:39 · answer #1 · answered by dragonball_z 2 · 0⤊ 0⤋
No fair requiring an algebriac solution ex post facto. Just drawing a sketch would indicate that the result is somewhere around pi/4
The comment is directed to the first mod by the questioner. Trial and error solutions is a field unfairly undertaught in math.
2007-12-06 17:37:19 · answer #2 · answered by cattbarf 7 · 1⤊ 0⤋
If you know calculus, you could use Newton's Method to find the root.
I checked the graphs and the intersection of y = cos x and y = x is near 0.8. I checked with Mathematica, and it could not find an algebraic solution. Instead, it was able to find a root near 0.8.
2007-12-06 17:26:12 · answer #3 · answered by Doug 2 · 0⤊ 0⤋
cos(x)=x
cos(x)-x=0
expand cos(x) using some series and solve.
x=0.74
with exact solution method:
Since u know
1) x is between 0 to 2pi and repeating.
2)cos(x) is between -1 to 1.
Maybe it is possible to use complex numbers method to find the exact solution.
2007-12-06 18:02:35 · answer #4 · answered by Anonymous · 0⤊ 0⤋