Question

已知sin（π/6+α）=4/5,α∈（π/3，5π/6），求cosα的值

Answer 1

π/3<α<5π/6,
π/2<π/6+α<π，则cos (π/6+α)<0
sin(π/6+α)=4/5, 则cos (π/6+α)=-3/5.

cosα=cos[(π/6+α)- π/6]
= cos (π/6+α) cosπ/6+ sin(π/6+α) sinπ/6
=-3/5*√3/2+4/5*1/2=(4-3√3)/10.

Answer 2

sin（pi/6+a）=4/5，a 属于（p/3，5p/6），
则 cos（pi/6+a）= －根号[1-(4/5)^2] = －3/5
sin（pi/6+a）= sin(pi/6)cosa + cos(pi/6)sina = (cosa)/2 + (根号3)(sina)/2 = 4/5
cos(a) + (根号3)(sina) = 8/5 ------------(1)
cos(pi/6+a）= cos(pi/6)cosa - sin(pi/6)sina = (根号3)(cosa)/2 - (sina)/2 = 3/5
(根号3)(cosa) - sina = －6/5 ---------------(2)
(1) + (2)*根号3 4*cosa = 8/5 + 6(根号3)/5 = (8－6根号3)/5
cos a = (4 －3根号3)/10

Answer 3

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