Question

已知sinθ+cosθ=1/2，求sin^3θ+cos^3θ的值。

步骤最重要，谢谢了！

Answer 1

令t=θ （我打着累啊）
sint+cost=1/2
(sint+cost)^2=1/4
sin^2t+2sintcost+cos^2t=1/4
1+2*sintcost=1/4
sintcost=-3/8

sin^3t+cos^3t
=(sint+cost)(sin^2t-sintcost+cos^2t)
=1/2*(1-(-3/8))
=11/16

Answer 2

(sint+cost)^2=1/4
1+2sintcost=1/4
sintcost=-3/8

(sint+cost)^3=1/8
(sint)^3+(cost)^3+3sintcost(sint+cost)=1/8
(sint)^3+(cost)^3=1/8-3sintcost(sint+cost)
=1/8-3*(-3/8)*1/4
=13/32

Answer 3

sin^3θ是sinθ的三次方吗？