已知cos(α+π/4)=3/5,π/2小于等于α<3π/2,求cos(2α+π/4)
已知cos(α+π/4)=3/5,π/2≤α<3π/2,求cos(2α+π/4)
π/2≤α<3π/2--->3π/4≤α+π/4<7π/4
cos(α+π/4)=3/5 > 0
--->3π/2<α+π/4<7π/4--->5π/4<α<3π/2--->5π/2<2α<3π
--->cos(2α+π/2)=2cos^(α+π/4)-1=2*9/25-1=-7/25=-sin(2α)
--->sin(2α)=7/25 --->cos(2α)=-24/25
--->cos(2α+π/4) = cos(2α)cos(π/4)-sin(2α)sin(π/4)
= (√2/2)(-...全部
已知cos(α+π/4)=3/5,π/2≤α<3π/2,求cos(2α+π/4)
π/2≤α<3π/2--->3π/4≤α+π/4<7π/4
cos(α+π/4)=3/5 > 0
--->3π/2<α+π/4<7π/4--->5π/4<α<3π/2--->5π/2<2α<3π
--->cos(2α+π/2)=2cos^(α+π/4)-1=2*9/25-1=-7/25=-sin(2α)
--->sin(2α)=7/25 --->cos(2α)=-24/25
--->cos(2α+π/4) = cos(2α)cos(π/4)-sin(2α)sin(π/4)
= (√2/2)(-24/25-7/25) = -16√2/25。
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