# SIMPLE:how do you solve (sin x)/x = 0.99

1. Jan 7, 2007

### LM741

how to you get this

thanks!!

2. Jan 7, 2007

### Integral

Staff Emeritus
There is no closed form solution. You might research something like a Newton's Method root finder. I did a quick fixed point interation and arrived at 0.24532 but it took over a 100 iterations to reach it.

I started with a guess of .5 and iterated

$$x = \frac { \sin x } {.99}$$

3. Jan 7, 2007

### waht

I did an approximation by hand,

Take the first terms of taylor series for sine

$$sin(x) = x - \frac { x^3 } {6} + \frac {x^5} {120}$$

$$\frac { \sin x } {x} = 1 - \frac { x^2 } {6} + \frac {x^4} {120} = 0.99$$

$$x^4 - 20x^2 + 1.2 = 0$$

Substitute, a = x^2

$$a^2 - 20a + 1.2 = 0$$

It's an easy quadratic equation, also got 0.2459674, and other solution 4.465366 which doesn't work.

Last edited: Jan 7, 2007
4. Jan 8, 2007

### Staff: Mentor

Thread moved to math homework forum.

5. Jan 8, 2007