Question

函数Y=SIN2X+COS2X的值域为多少？求解题过程

Answer 1

y=sin2x+cos2x=2^(1/2)sin(2x+180/4)
当2x+180/4=-180/2+k180即x=180/8+k180 sin（2x+180/4）有最小值-1所以y=2^(1/2)sin(2x+180/4)有最大值根号2 同理当x=-3*180/8+k180是y=根号2（2x+180/4）有最小值-跟2

Answer 2

Y=根号2*SIN(2X+45度）
值域【-根号2，根号2】

Answer 3

[负根号2，正根号2]

Answer 4

sin2x+cos2x
=√2(√2/2sin2x+√2/2*cos2x)
=√2(cospai/4sin2x+sinpai/4cos2x)
=√2sin(2x+pai/4)
所以...
公式:
cosasinb+sinacosb
=sin(a+b)
y=sin2x+cos2x
=√2(sin45sin2x+cos45cos2x)
=√2cos(45-2x)∈[-√2,√2]