Let P(x, y) be a general point on the circle x² + y² = 9 and let S be the point (3,0) as shown in the sketch below. %3D P(x, y) R Q(x, 0) S(3, 0) (i) Write down expressions for x and y in terms of 0. Hence, show that the area A of the shaded region R is 9 sin 20. 4 A = 30 – (ii) Use Newton's method to determine the value of 0 (in radians, to three decimal places) such that A = 2. f(xn) (Newton's method for solving f (x) = 0: xn+1 = xn° f'(xn) for n = 0, 1,2, ...)
Let P(x, y) be a general point on the circle x² + y² = 9 and let S be the point (3,0) as shown in the sketch below. %3D P(x, y) R Q(x, 0) S(3, 0) (i) Write down expressions for x and y in terms of 0. Hence, show that the area A of the shaded region R is 9 sin 20. 4 A = 30 – (ii) Use Newton's method to determine the value of 0 (in radians, to three decimal places) such that A = 2. f(xn) (Newton's method for solving f (x) = 0: xn+1 = xn° f'(xn) for n = 0, 1,2, ...)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(b) Let P(x, y) be a general point on the circle x² + y? = 9 and let S be the point
(3, 0) as shown in the sketch below.
P(x, y)
R.
Q(x, 0)
S(3,0)
(i) Write down expressions for x and y in terms of 0. Hence, show that the area
A of the shaded region R is
9.
-sin 20.
4
A = 30 –
(ii) Use Newton's method to determine the value of 0 (in radians, to three decimal
places) such that A = 2.
f (xn)
for n = 0, 1,2, ...)
f'(xn)
(Newton's method for solving f (x) = 0: xn+1 = Xn=
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