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Grade: 12
        how to compute roots of cos x =x
6 years ago

Answers : (2)

bharat bajaj
IIT Delhi
askIITians Faculty
122 Points
							The roots of this equation cannot be calculated exactly without using any program. But if you want to calculate its roots approximately, graphical method is the best method. Try this method and calculate the roots. It is easy.
Thanks
Bharat Bajaj
askiitians faculty
IIT Delhi
6 years ago
mycroft holmes
272 Points
							as a first approximation you could use a few terms from the taylor expansion of cos x.
So, x = 1 - x^2/2 gives us x = 0.73 which is close to the solution x = 0.7391

In fact, if you take a calculator take say x =1 and keep punching the cos key, you will arrive at this number (after around 80 steps max to get the accurate answer)

To know why this process works see Banach Fixed Point Theorem.
						
6 years ago
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