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Sin Series
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The program is written here to print the value of sine series. Sine series is a series which is used to find the value of sin(x). The expansion of the sine series is:
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Here ‘x’ is the angle of which the value is to be calculated and ‘n’ is the number of terms.
The value of ‘x’ will be taken as input from the user and the number of terms ‘n’ will also be taken as input.
The value of x is given in degree. Then it is converted into its equivalent radian. The value of the sine series is then calculated.
If the value of ‘x’ is 90 then the value of sin(x)=1.
Algorithm
INPUT: The value of the angle and the number of terms.
OUTPUT: The value of sin(x)
PROCESS:
Step 1: [Taking the input]
Read n [number of terms]
Read x [the angle for which the value is to be calculated]
Step 2: [Finding the value of sin(x)]
Set s<-1
Set sum<-0
[Finding the sum of the series]
For i=1 to n incremented by 2 repeat
Set f<-1
[Finding the factorial]
For j=1 to i repeat
Set f<-f×j
[Finding the sum of the series]
Set sum<-sum+s × xi/f
Set s<-s×(-1)
[End of ‘for’ loop]
Print "The value of sin(x) is sum"
Step 3: Stop.
Code
TIME COMPLEXITY:
for(i=1;i<=n;i=i+2)-----------------------------------O(n)
{
f=1;
//finding the factorial
for(j=1;j<=i;j++)----------------------------O(i)
f=f*j;
//finding the sum of the series
sum=sum+s*(pow(x,i)/f);
s=s*-1;
}
The time complexity of this program is O(n*i) where ‘n’ is the number of terms, ‘i’ is the power of each term.
SPACE COMPLEXITY:
The space complexity of this program is O(1) as it requires a constant number of spaces to execute the program for any given input.
