y=sin(2x+π/6),x∈[π/4,3π/4]求值域
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y=sin(2x+π/6),x∈[π/4,3π/4]求值域
y=sin(2x+π/6),x∈[π/4,3π/4]求值域
y=sin(2x+π/6),x∈[π/4,3π/4]求值域
画个sin函数的图像,再把2π/3
π/6<=x<=3π/4
π/3<=2x<=3π/2
π/2<=2x+π/6<=5π/3
π/2<=x<=3π/2
sinx是减函数
所以sin(3π/2)<=sin(2x+π/6)<=sin(π/2)
-1<=sin(2x+π/6)<=1
而sin(2x+π/6)值域本身就是[-1,1]
所以3π/2<=2x+π/6<=5π/3肯定...
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π/6<=x<=3π/4
π/3<=2x<=3π/2
π/2<=2x+π/6<=5π/3
π/2<=x<=3π/2
sinx是减函数
所以sin(3π/2)<=sin(2x+π/6)<=sin(π/2)
-1<=sin(2x+π/6)<=1
而sin(2x+π/6)值域本身就是[-1,1]
所以3π/2<=2x+π/6<=5π/3肯定也属于[-1,1]
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