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已知M(x,y)是圆x^2+y^2=1上任意一点,求y/(x+2)的取值范围
人气:493 ℃ 时间:2020-05-01 00:40:21
解答
设x=cosa y=sina 则:M=y/(x+2) = cosa/(sina+2)
cosa=Msina+2M
即:2M = cosa-Msina = √(M^2+1)sin[a+arctan(1/M)]
2M(max) = √(M^2+1)
即:4M^2 = M^2+1
M = ± √3/3
∴y/(x+2)的取值范围为:[ -√3/3,√3/3 ]
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