Question

已知tan a＝1/4,求sin∧3 a-cos∧3 a为

Answer 1

tana=1/4>0所以a 是一或三象限角,tana=1/4 可化为：sina/cosa=1/4,即 cosa=4sinasin^3(a)-cos^3(a)= sin^3(a)-64sin^3(a) = - 63sin^3(a)(1)当a是一象限角时,在a角的终边上取一点,（1,4）x=1,y=4r=√17sina=1/√17sin^3(a)=1/(17√17)=√17/289 - 63sin^3(a)= - 63√17/289即sin^3(a)-cos^3(a)= - 63√17/289(2)当a 是第三象限时,在a 角的终边上取一点(-1,-4)sina= - 1/√17;sin^3(a)= - √17/289sin^3(a)-cos^3(a)= 63√17/289