已知sinx=-5/13,x属于(派,3派/2),求sin(x-派/4)

已知sinx=-5/13,x属于(派,3派/2),求sin(x-派/4)
已知sinx=-5/13,x属于(派,3派/2),求sin(x-派/4)

已知sinx=-5/13,x属于(派,3派/2),求sin(x-派/4)
sinx=-5/13
x∈(П,3П/2)
cosx=√1-(-5/13)^2
=-12/13
sin(x-П/4)
=sinxcosП/4-cosxsinпП/4
=√2/2(-5/13+12/13)
=7√2/26