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Asked Nov 14, 2019
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Question 6 of 14
9n. Use Newton's Method to calculate 97t with xo = 27
The ninth positive solution of sin(x) = 0 is x
(Give your answers to six decimal places.)
Xз
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Question 6 of 14 9n. Use Newton's Method to calculate 97t with xo = 27 The ninth positive solution of sin(x) = 0 is x (Give your answers to six decimal places.) Xз

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Expert Answer

Step 1
Consider the given ninth positive solution of sinr 0 is x 97
Let the function be f(x) sinx and x 27
Calculate the derivative of f (x)=sinx as f'(x)
=COSx
f(x)
f(x,)
Note that, the Newton Raphson method is given by x= x
n+1
help_outline

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Consider the given ninth positive solution of sinr 0 is x 97 Let the function be f(x) sinx and x 27 Calculate the derivative of f (x)=sinx as f'(x) =COSx f(x) f(x,) Note that, the Newton Raphson method is given by x= x n+1

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Step 2
Now, compute the value of x using Newton Raphson method as follows
f(x)
f(x)
sin (27)
=27
cos(27
0.956376
30.273704
=27-
-0.292139
Now, compute the value of x, using Newton Raphson method as follows
f(x)
sin (30.273704)
cos(30.273704
= 30.273704
0.909559
32.462375
= 30.273704
0.415576
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Now, compute the value of x using Newton Raphson method as follows f(x) f(x) sin (27) =27 cos(27 0.956376 30.273704 =27- -0.292139 Now, compute the value of x, using Newton Raphson method as follows f(x) sin (30.273704) cos(30.273704 = 30.273704 0.909559 32.462375 = 30.273704 0.415576

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