a是锐角,且sin(a-π/6)=1/3,则cosa为

问题描述:

a是锐角,且sin(a-π/6)=1/3,则cosa为

sin(a-π/6)=1/3
sinacosπ/6-sinπ/6cosa=1/3
√3/2sina-cosa/2=1/3
√3sina-cosa=2/3
又sin²a+cos²a=1
∴sin²a+(√3sina-2/3)²=1
∴sina=(√3+2√2)/6

√3/2*sina-0.5cosa=1/3
27(1-cos^2a)=4+9cos^2a+12cosa
36cos^2a+12cosa-23=0
cosa=-1/6±[√12^2+4*6^2*23]/72
=-1/6±√6/6