作业帮已知函数f(x)=根号2(sinx-cosx),求(1)函数f(x)的值域(2)若函数的图象过(a,6/5),兀/4
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已知函数f(x)=根号2(sinx-cosx),求(1)函数f(x)的值域(2)若函数的图象过(a,6/5),兀/4
值域[-2,2] f(兀/4+a)= (3√2＋4√2)/5
1.
f(x)=2×[cos45sinx-cosxsin45)
f(x)=2×sin(x-45)
=2sin(x-π/4) 方式1
y=f(x)∈[-2,2]
2.
将（a,6/5)代入上面方式1，得sin(a-π/4)=3/5
将y=f(π/4+a)=2sin(a+π/4-π...
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1.
f(x)=2×[cos45sinx-cosxsin45)
f(x)=2×sin(x-45)
=2sin(x-π/4) 方式1
y=f(x)∈[-2,2]
2.
将（a,6/5)代入上面方式1，得sin(a-π/4)=3/5
将y=f(π/4+a)=2sin(a+π/4-π/4)=2sin(a-π/4+π/4)=2[sin(a-π/4)cosπ/4+cos(a-π/4)sinπ/4]
y=f(π/4+a)=2[√2/2sin(a-π/4)+√2 /2×cos(a-π/4)]=√2×(3/5+4/5)=7√2/5
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f(x)=2sin(x-45) 值域为[-2,2]
-兀/2+2k兀<=x-兀/4<=兀/2+2k兀
-兀/4+2k兀<=x<=3兀/4+2k兀
6/5=2sin(a-兀/4)
sin(a-兀/4)=3/5
兀/4
0
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f(x)=2sin(x-45) 值域为[-2,2]
-兀/2+2k兀<=x-兀/4<=兀/2+2k兀
-兀/4+2k兀<=x<=3兀/4+2k兀
6/5=2sin(a-兀/4)
sin(a-兀/4)=3/5
兀/4
0
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