Question

Write a Python program that verifies the formula with the help of the Python Math module. Note that the trigonometric functions in the module act on the angles in radians. Your program should perform the following steps 3 times:_____.

1. Pick a random number between 0 and 180 degrees representing an angle in degrees, say Dangle
2. Convert the angle from degrees to radians, say Rangle
3. Use the Math module to find and print the values of sin(Rangle) and cos(Rangle), and
4. Compute and print the value of the above expression: sin^2(Rangle) + cos^2(Rangle).
You can then visually verify if the result printed is 1 (or close to it).
Hint: angle_in_radians = (angle_in_degrees * Pi)/180

Answer 1

Written in Python

import math

import random

Dangle = random.randint(0,181)

pi = 22/7

Rangle = Dangle * pi/180

Rsin = math.sin(Rangle)

Rcos = math.cos(Rangle)

Result = Rsin**2 + Rcos**2

print("Result = "+str(Result))

Step-by-step explanation:

The next two lines import math and random library respectively

import math

import random

This line generates a random integer between 0 and 180

Dangle = random.randint(0,181)

This line initializes pi to 22/7

pi = 22/7

This line converts angle to radians

Rangle = Dangle * pi/180

The next two lines calculate the sin and cosine of the angle in radians

Rsin = math.sin(Rangle)

Rcos = math.cos(Rangle)

This line implements sin^2 theta + cos^2 theta

Result = Rsin**2 + Rcos**2

This line prints the required Result

print("Result = "+str(Result))