求cos a的值 (必修四数学)已知0<a<兀/3,cos(a+兀/6)=3/5,sin(a+兀/6)=4/5答案说cos a=(3根号3+4)/10
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求cos a的值 (必修四数学)已知0<a<兀/3,cos(a+兀/6)=3/5,sin(a+兀/6)=4/5答案说cos a=(3根号3+4)/10
求cos a的值 (必修四数学)
已知0<a<兀/3,cos(a+兀/6)=3/5,sin(a+兀/6)=4/5
答案说cos a=(3根号3+4)/10
求cos a的值 (必修四数学)已知0<a<兀/3,cos(a+兀/6)=3/5,sin(a+兀/6)=4/5答案说cos a=(3根号3+4)/10
cosa=cos(a+π/6-π/6)
=cos(a+π/6)cosπ/6+sin(a+π/6)sinπ/6
=(3/5)·(√3/2)(+4/5)·(1/2)
=(3√3+4)/10
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0<a<π/3
cos(a+π/6)=3/5
cosacosπ/6-sinasinπ/6=3/5
根号3/2cosa-1/2sina=3/5......(1)
sin(a+π/6)=4/5
sinacosπ/6+cosasinπ/6=4/5
根号3/2sina+1/2cosa=4/5......(2)
(1)*根号3 + (2):
3/2 cosa + 1/2 cosa = 3根号3/5 + 4/5
cosa = (3根号3+4)/10
对啊!
公式:cos(a-b)=cos(a)cos(b)+sin(a)sin(b) 已知:cos(a+兀/6)=3/5,sin(a+兀/6)=4/5
那么:cos(a)=cos[(a+π/6)-π/6]
=cos(a+π/6)cos(π/6)+sin(a+π/6)sin(π/6)
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对啊!
公式:cos(a-b)=cos(a)cos(b)+sin(a)sin(b) 已知:cos(a+兀/6)=3/5,sin(a+兀/6)=4/5
那么:cos(a)=cos[(a+π/6)-π/6]
=cos(a+π/6)cos(π/6)+sin(a+π/6)sin(π/6)
=3/5 X (根号3)/2 +4/5 X 1/2
=[3(根号3)+4]/10
因为:[3(根号3)+4]/10<1 符合条件:0<a<兀/3
故cos(a) =[3(根号3)+4]/10
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