11442. Sum of sines

Given a positive integer n and a real number x, find the value of the sum:

sin x + sin²x + … + sinⁿx

Input. Two numbers are given: a positive integer n (n ≤ 1000) and a real number x (∣x∣ ≤ 1000).

Output. Print the value of the specified sum, rounded to 6 decimal places.

Sample input	Sample output
3 1	2.145368

SOLUTION

loops

Algorithm analysis

Compute the specified sum using a loop.

At the i-th iteration, store the value sinⁱx in the variable t. At the i-th iteration, add the current term t = sinⁱx to the current value of the result res.

Algorithm implementation

Read the input data.

scanf("%d %lf", &n, &x);

Compute the value of the sum using a loop.

res = 0; t = 1;

for (i = 0; i < n; i++)

{

At the i-th iteration, it is necessary to multiply t by sin(x), and then add the current term t = sinⁱx to the result res.

t = t * sin(x);

res = res + t;

}

Print the answer.

printf("%lf\n", res);

Python implementation

import math

Read the input data.

n, x = input().split()

n = int(n)

x = float(x)

Compute the value of the sum using a loop.

res, t = 0, 1

for i in range(n):

At the i-th iteration, it is necessary to multiply t by sin(x), and then add the current term t = sinⁱx to the result res.

t *= math.sin(x)

res += t

Print the answer.

print(res)