testc.le

{Program to find cosine of a given number (radians)}
{please run with data of 1 radians and  20 terms }

begin     
    write('Recommended Input:'); writeln;
    write('1.0'); writeln;
    write('20.0'); writeln; writeln;

    counter:=0.0;                {Initialisation}
    xpower:=1.0;
    Answer:=1.0;
    fact:=1.0;
    sign:=0.0-1.0;
       	
    write('Program to calculate the cosine of a given number using a taylor expansion');
    writeln;
    write('Please enter the number: ');
    read(x);
    writeln;
    write('Please enter the number of terms to be used in the expansion(>1).');
    writeln;
    write('Note large numbers (>20) may cause floating point overflow: ');
    read(accuracy);
    writeln;
    
    if accuracy>1.0  {Catch the case where the number of taylor terms is not larger than one}
	begin
		repeat	{This loop adds successive taylor terms}
        		begin
				xpower:=xpower*x*x*sign;		{sign ensures the +ve -ve +ve aspect of series}
				counter:=counter+2.0;		{factorial number increments by two each time}
				fact:=fact*counter*(counter-1.0);{Calculate factorial number incrementally}
				accuracy:=accuracy-1.0;
				Answer:=Answer+(xpower/fact);	{Increment the new estimate of cos(x)}
   	 		end
		until accuracy<0.0;  {repeat}
    	
		write('(Approximate) answer: ');			{Output the approx. answer}
    		write(Answer);
    		writeln;
   	end 
    else
	begin
		write('The number of terms given must be larger than 1');	{Catch the fall through case}
    		writeln;
	end;
 
end