∵sinθ+cosθ=-1/5
∴(sinθ+cosθ)²=1/25
1+2sinθcosθ=1/25
2sinθcosθ=-24/25
sinθcosθ=-12/25
(1)sin³θ+cos³θ
=(sinθ+cosθ)(sin²θ-sinθcosθ+cos²θ)
=-1/5[1-(-12/25)]
=-1/5*37/25
=-37/125
(2)sin四次方θ+cos四次方θ
=(sin²θ+cos²θ)²-2sin²θcos²θ
=1-2(-12/25)²
=1-2*144/625
=1-288/625
=337/625