求6/5(sinθ+cosθ)-sinθ*cosθ的最大值和最小值
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求6/5(sinθ+cosθ)-sinθ*cosθ的最大值和最小值
0<θ<90°
0<θ<90°
原式=6/5[sinθ+sin(π/2-θ)]- sin(2θ)/2
=12/5[sin(π/4) cos(θ-π/4)]- sin(2θ)/2
=6√2/5 cos(θ-π/4)-cos(2θ-π/2)/2
=6√2/5 cos(θ-π/4)-{2 [cos(θ-π/4)]^2-1}/2
=-[cos(θ-π/4)]^2+6√2/5 cos(θ-π/4)+1/2
=-{[cos(θ-π/4)]^2-6√2/5 cos(θ-π/4)+ [3√2/5 ]^2}+1/2-[3√2/5 ]^2
=-{[cos(θ-π/4)]- 3√2/5}^2-11/50
在0
=12/5[sin(π/4) cos(θ-π/4)]- sin(2θ)/2
=6√2/5 cos(θ-π/4)-cos(2θ-π/2)/2
=6√2/5 cos(θ-π/4)-{2 [cos(θ-π/4)]^2-1}/2
=-[cos(θ-π/4)]^2+6√2/5 cos(θ-π/4)+1/2
=-{[cos(θ-π/4)]^2-6√2/5 cos(θ-π/4)+ [3√2/5 ]^2}+1/2-[3√2/5 ]^2
=-{[cos(θ-π/4)]- 3√2/5}^2-11/50
在0
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