The exact solution of cosx x, how to solve the equation cosx x?

Because cosx=1-x 2 2!+x^4/4!-x^6/6!+x^8/8!..

is the root of a polynomial with rational coefficients of an infinite term, so it cannot be expressed (transcendence), so it can only be approximated.

Newton's Iterative Method:

Let f(x)=cosx-x=0

f'(x)=-sinx-1

Shilling x=1x=1-(cos1-1) (-sin1-1)=Second iteration:

x=After many iterations, x= is obtained, and the error is less than 1e-10

You're crazy about advanced math, aren't you?

All of them have solved the transcendent equation ......

Method 1: Check the cosine function table.

Method 2: Enter any number in the calculator, take the cos value, and get the value accurate to 10 decimal places when the number remains unchanged.

Method 3: Newton's Law. I can't say clearly, just a rough idea.

Take an approximate value for the equation f(x)=x-cosx=0. Take the initial value x0=a so that f(a) > 0 (because f"(x)>0), and |f'(x0)|^2>|f"(xo)f(xo)/2|。The tangent of the curve (y-f(a)) (x-a)=f'(a), which intersects with the x-axis is x=a-f(a) f'(a)。

Use the iterative formula xn+1=xn-f(xn) f'(xn) is gradually approaching.

Since the range of cosx is -1,1, -1<=x<=1.

1 rad = 180 degrees.

That is, the range of cosx is (cos(degree), cos(degree))cos57=

The cosx range is (,

Let f(x)=cosx-xthen f'(x)=-sinx-1<=0, so f(x) is monotonically reduced, with at most only one zero point.

f(0)=1>0

f(1)=cos1-1<0

Therefore there is a unique zero point, and it is in the interval (0,1).

Differential equationsA differential equation is an equation that describes the relationship between the derivative of an unknown function and an independent variable. The solution of a differential equation is a function that conforms to the equation. In elementary mathematics, the solution of an algebraic equation is a constant value.

Differential equations are mathematical equations that relate some functions to their derivatives. In applications, functions usually represent physical quantities and derivatives represent their rates of change, and equations define the relationship between the two. Because this relationship is so common, differential equations play a prominent role in many disciplines, including engineering, physics, economics, and biology.

Judging from the drawing, Lu Shen can only take an approximate value, which is about.

Let f(x)=x-cosx, then.

f'(x)=1+sinx 0, so f(x) is the only solution of the multiplier function, f(x)=0.

f(,f(,f(,f(,f(,,so far,skin, x, if filial piety grip only skin beat needs, also filial piety grip only limb can be skillfully cultivated and pinned skillfully to improve accuracy.

Multiple revisions didn't work, I don't know why.

The specific process is as follows: sin2x+cos2x= 2[( Xun Chichang 2 Danzi 2)sin2x+( 2 2)cos2x] =2[cos45°sin2x+sin45°cos2x] = mu chop 2sin(2x+45°)

Alas. Find a socks to sell input method for pants hidden, and so many people answered.

cosx 0, that is, pure comic x in.

1. Four quadrants.

So x (2k - 2, 2k + 2), k z

0 73908513321516064165531208767387 there is no way to solve it with the mathematical methods of middle school, and can only use the method of approximating the solution of the square hole without family program in advanced mathematics, the original equation becomes [(cosx) x]-1=0, let f(x)=(cosx x)-1 and then find the derivative, f'(x) and f"(x) find the invariant sign, and between and 1 x1=1-f(..

cosx>-1 solution x value range.

Because the answer cosx is only equal to -1 when x is on the abscissa axis to the left of the coordinate origin, and all other points have cosx> qingchai liang -1, so x is a real number and is not equal to (1+2k).