函数y=tanπ/4-sin5π/4(7π/4+2x),x∈r. 求1.函数的最大值最小值 2函数的最小正周期 3.函数的单调区间
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y=tanπ/4-sin5π/4(7π/4+2x)=1-sin(35π/16+5π/2 x)=1-sin(3π/16+5π/2 x)
(1)因为-1<=sin(3π/16+5π/2 x)<=1，所以y (max)=1-(-1)=2,y(min)=1-1=0
(2)最小正周期T=2π/(5π/2)=4/5
(3)由2kπ-π/2<=3π/16+5π/2 x<=2kπ+π/2得4/5k-19/40<=x<=4/5k+1/8
由2kπ+π/2<=3π/16+5π/2 x<=2kπ+3π/2得4/5k+1/8<=x<=4/5k+21/40
故函数的单调增区间为（4/5k+1/8，4/5k+21/40），单调减区间为（4/5k-19/40，4/5k+1/8）
(1)因为-1<=sin(3π/16+5π/2 x)<=1，所以y (max)=1-(-1)=2,y(min)=1-1=0
(2)最小正周期T=2π/(5π/2)=4/5
(3)由2kπ-π/2<=3π/16+5π/2 x<=2kπ+π/2得4/5k-19/40<=x<=4/5k+1/8
由2kπ+π/2<=3π/16+5π/2 x<=2kπ+3π/2得4/5k+1/8<=x<=4/5k+21/40
故函数的单调增区间为（4/5k+1/8，4/5k+21/40），单调减区间为（4/5k-19/40，4/5k+1/8）
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