How to solve this?

  • Thread starter Werg22
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  • #1
Werg22
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Two simple waves but on is a Y function and the other a X function, on do you find the intersecting point?

y=cos(x)
x=cos(y)

cos^-1(x)=cos(x)
 

Answers and Replies

  • #2
VietDao29
Homework Helper
1,426
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You can use Newton's method to solve this:
[tex]x_n = \frac{f(x_{n - 1})}{f'(x_{n - 1})}[/tex]
And the solution x is:
[tex]x = \lim_{n \rightarrow \infty} x_n[/tex]
Newton's method
You can change the equation a bit so it's easier to take the dirivative of the function:
Since the graph of Arccos(x) is the reflection of the graph Cos(x) across the line y = x.
So the intersection of the two graph Arccos(x) and Cos(x) is right on the line y = x. So the equation can be changed to:
[tex]\cos(x) = x \Leftrightarrow \cos(x) - x = 0[/tex]
Let f(x) = cos(x) - x.
So f'(x) = -sin(x) - 1.
Using the formula, you have:
[tex]x_n = \frac{\cos (x_{n - 1}) - x_{n - 1}}{-\sin (x_{n - 1}) - 1}[/tex]
Since the two graph cos(x) and x will cut each other at some x lies between 0, and pi. So you just choose [tex]x_0 \in [0, \ \pi][/tex], eg: x_0 = 0.5,...
Viet Dao,
 
Last edited:

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