已知Sin(A+B)=33/65 cosB=5/13 如題

已知Sin(A+B)=33/65 cosB=5/13 如題

sin(A+B)= sinAcosB+cosAsinB,sin^2A+cos^2A=1 sin^2B+cos^2B=1囙此:sin(A+B)=sinA*cosB+√(1-sin^2A)*√(1-cos^2B)=33/65 =sinA*5/13+√(1-sin^2A)*√1-(5/13)^2=33/65∴sinA=0.9477