y=2sin^2x-sinxcosx+3cos^2x 求值域

题目

y=2sin^2x-sinxcosx+3cos^2x 求值域

答案

解y=2sin²x-sinxcosx+3cos²x =(2sin²x+2cos²x)-1/2(2sinxcosx)+cos²x =2-1/2sin2x+1/2(2cos²x-1)+1/2 =1/2cos2x-1/2sin2x+5/2 =√2/2(cos2xcosπ/4+sinπ/4sin2x)+5/2 =√2/2cos...