Tau Day MMXVIII (#199)

                                     int
        O=19,I=19;typedef long double f 
    ;long fac(long n){return n?n--*fac( 
  n):1;}f pow(f x,int p){return p--?x   
 *pow(x,p):1;}f sin(f x){f v=0;for      
(int           k=~0;++k                 
<=             O;)k%2&&                 
              (v+=(~-k                  
             %4?-1:1)*                  
             pow(x,k)                   
            /fac(k));                   
            return v                    
           ;}main()                     
           {f a=6,b                     
          =7, tau;                      
          for (int                      
         j=~0;++j                       
         <I;)sin(           tau         
        =a+(b-a)           /2           
        )>0? (b=          tau           
        ):(a=tau        )  ;            
        printf (      "%ca"             
        "u ~ %.*Lf",116,                
           O,tau);}                     

Try it online!

Happy tau day.