cosX=-12/13,cos(X+Y)=17根号2/26,X属于π到3/2π,X+Y属于3/2π到2π.求Y

题目

cosX=-12/13,cos(X+Y)=17根号2/26,X属于π到3/2π,X+Y属于3/2π到2π.求Y

答案

X属于π到3/2π cosX=-12/13 sinX=-5/13
X+Y属于3/2π到2π cos(X+Y)=17根号2/26 sin(x+y)=-7√2/26
cosy=cos[(x+y)-x]=cos(x+y)cosx+sin(x+y)sinx
=(-12*17√2+35√2)/26*13
=-169√2/26*13
=-√2/2
X属于π到3/2π,X+Y属于3/2π到2π 0所以y=3π/4