Question

известно что sint+cost=0,6.вычислите:sin^3t+cos^3t

Answer 1

$sint cos t=\frac{sin^2 t +2sin t cos t +cos^2t-1}{2}=\frac{(sin t +cos t)^2-1}{2}=\frac{0.6^2-1}{2}=\frac{0.36-1}{2}=\frac{-0.64}{2}=-0.32; \\ sin^3t+cos^3t=(sin t+ cos t)(sin^2 t-cost sin t+cos^2 t)=\\0.6*(1-(-0.32))=0.6*1.32=0.792$

Answer 2

(sint+cost)^2=(0,6)^2    1+sin2t=0.36    sin2t=-0.64

 

sin^3t+cos^3t=(sint+cost)(sin^2t-sintcost+cos^2t)= 0.6*(1-sin2t)=0.6*(1+0.64)=

=0.6*1.64=0.984