已知XY满十足X^2/16+Y^2/9=1,求X+Y的取值范围

Question

已知XY满十足X^2/16+Y^2/9=1,求X+Y的取值范围

Answer 1

令x=4sina,y=3cosa
则x+y=√(4^2+3^2)sin(a+b)=5sin(a+b),其中,tgb=3/4
sin(a+b)属于[-1,1]
因此x+y的取值范围为[-5,5]