Question

PLEASE USE PYTHON CODE

7. determine the two roots of sinx+3cosx-2 =0 that lie in the interval (-2,2). use the Newton- Raphson method and solve by the secant formula

Answer 1

# Program to find root of an equations using secant method

# function takes value of x

# and returns f(x)

import math

def f(x):

# we are taking equation as sinx+3cosx-2

f = math.sin(x)+3*math.cos(x)-2

return f;

def secant(x1, x2, E):

n = 0; xm = 0; x0 = 0; c = 0;

if (f(x1) * f(x2) < 0):

while True:

# calculate the intermediate value

x0 = ((x1 * f(x2) - x2 * f(x1)) /

(f(x2) - f(x1)));

# check if x0 is root of

# equation or not

c = f(x1) * f(x0);

# update the value of interval

x1 = x2;

x2 = x0;

# update number of iteration

n += 1;

# if x0 is the root of equation

# then break the loop

if (c == 0):

break;

xm = ((x1 * f(x2) - x2 * f(x1)) /(f(x2) - f(x1)));

if(abs(xm - x0) < E):

break;

print("Root of the given equation =", round(x0, 6));

print("No. of iterations = ", n);

else:

print("Can not find a root in the given inteval");

# Driver code

# initializing the values

x1 = 0;

x2 = 90;

E = 0.0001;

secant(x1,x2, E);

Please refer the snap given below for indentation: