已知方程sin^2x+cosx+a=0有实数解,则a的取值范围是_________
热心网友
sin^x+cosx+a=01-cos^x+cosx+a=0cos^x-cosx=(1+a)----(cosx-1/2)^=5/4+a∵cosx∈[-1,1],∴cosx-1/2∈[-3/2,1/2]∴(cosx-1/2)^∈[0,9/4]5/4+a∈[0,9/4]∴a∈[-5/4,1]
已知方程sin^2x+cosx+a=0有实数解,则a的取值范围是_________
sin^x+cosx+a=01-cos^x+cosx+a=0cos^x-cosx=(1+a)----(cosx-1/2)^=5/4+a∵cosx∈[-1,1],∴cosx-1/2∈[-3/2,1/2]∴(cosx-1/2)^∈[0,9/4]5/4+a∈[0,9/4]∴a∈[-5/4,1]