PLT OF AN AIR AMBULANCE HELI REQUESTS SVFR THROUGH CLASS B AIRSPACE. THERE IS NO SUCH OPTION AVAILABLE AT THIS ARPT AND CTLR ASKS ON COURSE HDG THEN ISSUES SQUAWK CODE AND CLRS RPTR TO CONTINUE ON HDG. LATER; CTLR INDICATES RPTR IS FLYING A DIFFERENT HDG THAN STATED. ALL IN ACFT AGREE THAT PLT STATED THE HDG HE WAS FLYING.

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ON AN EMS MISSION FROM XYZ TO ABC; THE WX AT XYZ WAS VFR AND THE WX AT ABC WAS VFR. BUT ENRTE; ZZZ WENT IFR. VISIBILITY DOWN TO 2 1/2 MI. I REQUESTED AN SVFR CLRNC THROUGH THE CLASS B AIRSPACE; NOT SEEING ON THE SECTIONAL; SVFR WAS NOT AUTH. THE CTLR TOLD ME THAT FACT; AND SAID I WAS UNDER THE CLASS B AIRSPACE. HE ASKED ME WHAT MY ON COURSE HDG WAS AND I TOLD HIM 020 DEGS. HE SAID TO FLY THAT HDG AND HE WOULD WORK ME THROUGH THE CLASS B AIRSPACE WHEN I GOT TO IT. APPROX 5 MINS LATER HE CALLED AND ASKED MY HDG. I SAW 020 DEGS. HE SAID I HAD TOLD HIM MY ON COURSE HDG WOULD BE 010 DEGS AND I WAS HDG TOWARD HIS TKOF AND LNDG CORRIDORS. HE THEN ADVISED ME TO CONTACT YYY TWR AND GO THROUGH HIS CLASS D AIRSPACE. MY DOCTOR AND NURSE CONFIRMED TO ME THAT I HAD INDEED TOLD THE CTLR THAT MY ON COURSE HDG WOULD BE 020 DEGS AND NOT 010 DEGS AS HE HAD THOUGHT. I THEN CONTACTED YYY AND ASKED FOR CLRNC THROUGH THEIR CLASS D AIRSPACE. I TOLD THEM I WAS APPROX 10 MI S. I THEN PUT YYY IN THE GPS AND NOTED I WAS 4.86 NM FROM YYY SO I FIGURED I MUST HAVE BEEN ABOUT 6 NM S WHEN I CALLED. I CALLED YYY AND INFORMED THEM OF MY MISTAKE. THEY SAID THEY KNEW BECAUSE THEY HAD ME ON RADAR WITH A CODE OF XXXX. I HAD ALREADY CHANGED BACK TO 1200 BY THAT TIME BECAUSE ZZZ APCH HAD CUT ME LOOSE. THEY ASKED ME TO PUT CODE XXXX BACK IN THE XPONDER SO THEY COULD HAND ME OFF TO ZZZ APCH N OF YYY. I DID AND THERE WERE NO FURTHER PROBS. THERE WAS NO CONFLICT WITH TFC AT EITHER ZZZ OR YYY.