Sine series : sin x = x - ((x^3)/3!) +
((x^5)/5!) - …………..
Cosine Series : cos x = 1 - ((x^2)/2!) + ((x^4)/4!)
-…………...
Exponential Series : e^x =
1 + (x/1!) + ((x^2)/2!) + ((x^3)/3!)+…….
Algorithm
Step 1:Start
Step
2:Declare variables i,n,j,ch as integers ;x,t,s,r as float and c=’y’ as char.
Step
3:while c=’y’ repeat steps 4 to 13
Step
4:Print the menu 1.Sine 2.Cosine 3.Exponential series.
Step
5:Input and read the choice,ch.
Step
6:If ch=1 then
6.1)Input and read the
limit of the sine series,n.
6.2)Input and read the
value of angle(in degree),x.
6.3)Convert the angle
in degree to radian,x=((x*3.1415)/180)
6.4)Assign t=r and s=r.
6.5)Initialize i as 2.
6.6)Initialize j as 2.
6.7)while(j<=n) repeat the
steps a to d.
a)Find
t=(t*(-1)*r*r)/(i*(i+1))
b)Find
s=s+t
c)Increment
i by 2.
d)Increment
j by 1.
6.8)End while.
6.9)Print the sum of
the sine series,s.
Step
7:End if.
Step
8:Else If the ch=2 then
8.1)Input and read the
limit of the cosine series,n.
8.2)Input and read the
value of angle(in degree),x.
8.3)Convert the angle
in degree to radian,x=((x*3.1415)/180)
8.4)Initialize t as 1,s
as 1 and i as 1.
8.5)Initialize j as 2.
8.6)while(j<=n) repeat the
steps a to d.
a)Find
t=(t*(-1)*r*r)/(i*(i+1))
b)Find
s=s+t
c)Increment
i by 2.
d)Increment
j by 1.
8.7)End while.
8.8)Print the sum of
the cosine series,s.
Step
9:End if.
Step
10:Else If ch=3 then
10.1)Input and read the
limit of the exponential series,n.
10.2)Input and read the
value of power of exponential series,x.
10.3)Initialize t as1
and s as 1.
10.4)Initialize i as 1.
10.5)while(i<n) repeat the
steps a to c.
a)Find
t=(t*x)/i
b)Find
s=s+t
c)Increment
i by 1.
10.6)End while.
10.7)Print the sum of
the exponential series,s.
Step
11:End if.
Step
12:Print ‘wrong choice’.
Step
13:End while.
Step
14:Stop.
Program
#include<stdio.h>
#include<conio.h>
void main()
{
int i,n,j,ch;
float x,t,s,r;
char c='y';
clrscr();
do
{
printf("\n1.SINE SERIES");
printf("\n2.COSINE SERIES");
printf("\n3.EXPONENTIAL SERIES");
printf("\n ENTER THE CHOICE");
scanf("%d",&ch);
switch(ch)
{
case 1:
printf("\nENTER THE LIMIT");
scanf("%d",&n);
printf("\nENTER THE VALUE OF x:");
scanf("%f",&x);
r=((x*3.1415)/180);
t=r;
s=r;
i=2;
for(j=2;j<=n;j++)
{
t=(t*(-1)*r*r)/(i*(i+1));
s=s+t;
i=i+2;
}
printf("\nSUM OF THE GIVEN SINE SERIES IS %4f",s);
break;
case 2:
printf("\nENTER THE LIMIT ");
scanf("%d",&n);
printf("\nENTER THE VALUE OF x:");
scanf("%f",&x);
r=((x*3.14)/180);
t=1;
s=1;
i=1;
for(j=2;j<=n;j++)
{
t=((-1)*t*r*r)/(i*(i+1));
s=s+t;
i=i+2;
}
printf("\n SUM OF THE COSINE SERIES IS %f",s);
break;
case 3:
printf("\nENTER THE LIMIT");
scanf("%d",&n);
printf("\nENTER THE VALUE OF x:");
scanf("%f",&x);
t=1;
s=1;
for(i=1;i<n;i++)
{
t=(t*x)/i;
s=s+t;
}
printf("\nSUM OF EXPONENTIAL SERIES IS %f",s);
break;
default:
printf("\n WRONG CHOICE");
}
printf("\n DO U WANT TO CONTINUE Y/N");
scanf("%c",&c);
}
while(c=='y');
getch();
}
Output
1.SINE SERIES
2.COSINE SERIES
3.EXPONENTIAL SERIES
ENTER THE CHOICE 1
ENTER THE LIMIT 2
ENTER THE VALUE OF x:60
SUM OF THE GIVEN SINE SERIES IS 0.855787
DO U WANT TO CONTINUE Y/N y
1.SINE SERIES
2.COSINE SERIES
3.EXPONENTIAL SERIES
ENTER THE CHOICE 2
ENTER THE LIMIT 2
ENTER THE VALUE OF x:60
SUM OF THE COSINE SERIES IS 0.452245
DO U WANT TO CONTINUE Y/N y
1.SINE SERIES
2.COSINE SERIES
3.EXPONENTIAL SERIES
ENTER THE CHOICE 3
ENTER THE LIMIT 2
ENTER THE VALUE OF x:3
SUM OF EXPONENTIAL SERIES IS 4.000000
DO U WANT TO CONTINUE Y/N n
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