计算cos(1/2arctan(-3/4))

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计算cos(1/2arctan(-3/4))
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计算cos(1/2arctan(-3/4))
计算cos(1/2arctan(-3/4))

计算cos(1/2arctan(-3/4))
cos(1/2arctan(-3/4))
=cos(1/2*(-36.8699))
=cos(-18.435)
=0.948683

设arctan(-3/4)=2x
2x∈(-π/2,0)
x∈(-π/4,0)
那么tan2x=-3/4
sin2x=-3/5
cos2x=4/5
cos2x=2cos²x-1=4/5
cos²x=9/10
cosx>0 cosx=3根号10/10
cos(1/2arctan(-3/4)))=cosx=3根号10/10

设arctan(-3/4)=a
tana=-3/4,a∈(-π/2,0]
x/2∈(-π/4,0]
cosa/2=根号1+cosa/2
cosa=4/5
cosa/2=根号(1+4/5)/2=
3根号10/10