已知sin(pai/6+a)=3/5,pai/3

已知sin(pai/6+a)=3/5,pai/3
已知sin(pai/6+a)=3/5,pai/3

已知sin(pai/6+a)=3/5,pai/3
因为π/3

sin(π/6+a)=3/5
sina=sin(π/6+a-π/6)=sin(π/6+a)cosπ/6-cos(π/6+a)sinπ/6
π/3＜a＜5π/6
π/2＜a+π/6＜π
∴cos(π/6+a)=-4/5
sin(π/6+a)cosπ/6-cos(π/6+a)sinπ/6
=(3/5)*(√3/2)+(4/5)*(1/2)
=(4+3√3)/10
cosa=1-(sina)^2=1-[(4+3√3)/10]^2=(57-24√)/100