The Newton Rapson Method

Task 1
Task 1 (1)
(a) Frequency = (4/3)/(2*pi) = 0.21 Hz
Period = 1/ Frequency = 1/0.21 = 4.76 sec
Amplitude = 10
(b) Frequency = (3)/(2*pi) = 0.47 Hz
Period = 1/ Frequency = 1/0.47 = 2.12 sec
Amplitude = 10
(c) Assuming
2 = Rcos α.........................(1)
√3 = Rsin α........................(2)
Solving 1 and 2 we get,
R = √7
α = tan-1 (√3/2)
so we can write
Rsin (x + α) = √7 sin (x + tan-1 (√3/2))
( d) To solve cos2(x) - sin2(x) = 1..............................(1)
Since cos2(x) = 1- sin2(x)
So we an write (1) as
1-2 sin2(x) = 1
-2 sin2(x) = 0
Sin(x) = 0

Hence,
x = 0
or
x = n*pi (where n is an integer)

Task 2
Task 2 (2)
The given system is
12.6x1 + 7.9x2 + 6.2x3 = 18
4.8x1 + 4.8x2 + 7.5x3 = 6.39
-13x1 + 3.5x2 + 13x3 = -17.4
We can write the system as

So h n wt e a s er is