请问y=4倍根号2*sinXcosX+cos2X值域怎么求?关键是步骤,..X是属于【0,90】
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![请问y=4倍根号2*sinXcosX+cos2X值域怎么求?关键是步骤,..X是属于【0,90】](/uploads/image/z/8558354-2-4.jpg?t=%E8%AF%B7%E9%97%AEy%3D4%E5%80%8D%E6%A0%B9%E5%8F%B72%2AsinXcosX%2Bcos2X%E5%80%BC%E5%9F%9F%E6%80%8E%E4%B9%88%E6%B1%82%3F%E5%85%B3%E9%94%AE%E6%98%AF%E6%AD%A5%E9%AA%A4%2C..X%E6%98%AF%E5%B1%9E%E4%BA%8E%E3%80%900%2C90%E3%80%91)
请问y=4倍根号2*sinXcosX+cos2X值域怎么求?关键是步骤,..X是属于【0,90】
请问y=4倍根号2*sinXcosX+cos2X值域怎么求?
关键是步骤,..X是属于【0,90】
请问y=4倍根号2*sinXcosX+cos2X值域怎么求?关键是步骤,..X是属于【0,90】
y=4倍根号2*sinXcosX+cos2X
=2倍根号2*sin2X+cos2X
=3*(2倍根号2/3*sin2X+1/3cos2X)(令tanφ=1/2倍根号2)
=3*[sin(2X+φ)]
因为X是属于【0,90】,那么2X+φ属于【φ,180+φ】,正好半个周期
所以y的最大值应是1*3=3,
其最小值应是3*sin(180+φ)=-3*sinφ=-3*1/3=-1
所以y=4倍根号2*sinXcosX+cos2X值域应是[-1,3]
sinXcosX=1/2(sin2X)