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

  • Thread starter LM741
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In summary, the conversation discusses finding the value of 0.24 in radians and suggests using methods such as Newton's Method or a fixed point iteration. The speaker also shares their own approximation using the first terms of the Taylor series for sine and solving a quadratic equation. The conversation ends with a request for more information or clues about the solution.
  • #1
LM741
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the answer is 0.24 (working in radians)

how to you get this

thanks!
 
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  • #2
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

[tex] x = \frac { \sin x } {.99} [/tex]
 
  • #3
I did an approximation by hand,

Take the first terms of taylor series for sine

[tex] sin(x) = x - \frac { x^3 } {6} + \frac {x^5} {120} [/tex]

[tex] \frac { \sin x } {x} = 1 - \frac { x^2 } {6} + \frac {x^4} {120} = 0.99 [/tex]

[tex] x^4 - 20x^2 + 1.2 = 0 [/tex]

Substitute, a = x^2

[tex] a^2 - 20a + 1.2 = 0 [/tex]It's an easy quadratic equation, also got 0.2459674, and other solution 4.465366 which doesn't work.
 
Last edited:
  • #4
Thread moved to math homework forum.
 
  • #5
willyf1 said:
I looked for docs that referring to this problem but couldn't find any of those, do you have a clue?

What about waht's solution?
 

1. What does the equation (sin x)/x = 0.99 mean?

The equation (sin x)/x = 0.99 represents a mathematical relationship between the sine function and the variable x, where the result of dividing the sine of x by x is equal to 0.99.

2. How do you solve for x in the equation (sin x)/x = 0.99?

To solve for x in this equation, we can use algebraic manipulation and the properties of sine and cosine functions. First, we multiply both sides by x to get sin x = 0.99x. Then, we use the inverse sine function to isolate x, giving us x = sin^-1(0.99x). Finally, we can use a calculator to find the value of x.

3. Are there any special techniques or formulas needed to solve this equation?

No, there are no special techniques or formulas needed to solve this equation. It can be solved using basic algebra and the inverse sine function.

4. How many solutions are there for the equation (sin x)/x = 0.99?

There are infinitely many solutions for this equation. Since the sine function is periodic, there are multiple values of x that satisfy the equation. However, when using a calculator, it will typically only give one solution within a certain range.

5. Can this equation be solved without using a calculator?

Yes, this equation can be solved without a calculator by using trigonometric tables or by using trigonometric identities and approximations. However, using a calculator will provide a more accurate solution.

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