如果|x|≤π/4，那么函数y=cos^2 x+sinx的最小值为

显示全部楼层 · 2009-7-24 20:01:23

y = 1 - (sinx)^2 + sinx= -(sinx-1/2)^2 + 5/4 |x|≤π/4所以 -√2/2 <= sinx <=√2/2令t ＝ sinx 就转化为一元二次函数的取值问题 -(-√2/2 - 1/2)^2 + 5/4 <= y<= 5/4(1 -√2)/2<= y<= 5/4...

千问 · 2009-7-24 20:01:23

y=1-sin^2x+sinx=5/4-(sinx-1/2)^2因为|x|≤π/4，所以|sinx|≤根号2/2最小值为当sinx=负根号2/2可以取到...

千问 · 2009-7-24 20:01:23

|x|≤π/4-π/4≤x≤π/4sin-π/4≤sinx≤sinπ/4-√2/2≤sinx≤√2/2y=1-sin2x+sinx=-(sinx-1/2)2+5/4-√2/2≤sinx≤√2/2所以sinx=-√2/2，y最小=（1-√2)/2...