已知cos(a-pai/3)=3/5,a为锐角,求sina
来源：学生作业帮助网 编辑：六六作业网 时间：2024/12/24 05:13:45
已知cos(a-pai/3)=3/5,a为锐角,求sina
已知cos(a-pai/3)=3/5,a为锐角,求sina
已知cos(a-pai/3)=3/5,a为锐角,求sina
cos(a-pai/3)=3/5
cosasinpai/3+sinacospai/3=3/5
根号3/2cosa+1/2sina=3/5
根号3/2根号(1-sin^2a)=3/5-1/2sina
同＊10
5根号3根号(1-sin^2a)=6-5sina
平方：
75(1-sin^2a)=36-60sina+25sin^2a
0=-39-60sina+100sin^2a
sina=(60+根号(19200))/200=(60+根号(16*4*3*100))/200=(60+80根号3)/200=(3+4根号3)/10
cos(a-π/3)=3/5 sin(a-π/3)=4/5
∴sina=sin[(a-π/3)+π/3]
=sin(a-π/3)cos(π/3)+cos(a-π/3)sin(π/3)
=(4/5)×(1/2)+(3/5)×(√3/2)
=(4+3√3)/10
∵-π/3
∴sina=sin[(a-π/3)+π/3]
=sin(a-π/3)cos(π/3)+cos(a-π/3)sin(π/3)
=(-4/5)(1/2)+(3/5)(√3/2)
=(3√3-4)/10
a为锐角.a-π/3∈（-π/3,π/6)
cos(a-π/3)=3/5
sin（a-π/3)=根号(1-cos^2(a-π/3)=4/5或sin（α-π/3)= -4/5
sina=sin[(a-π/3)+π/3]=sin(a-π/3)cosπ/3+cos(a-π/3)sinπ/3
=4/5*1/2+3/5*根号3/2=(4+3根号3)/10
sina=(4+3根号3)/10 或 sina=(4-3根号3)/10