Question

f(x)=sin(x-π/6）.已知a,b属于(0,2分之派,且f(a)=5分之3,f(b)=13分之12,求f(a-b

Answer 1

a,b属于(0,π/2)

a-π/6,b-π/6属于(-π/6,π/3)

sin(a-π/6）=3/5

cos(a-π/6）=4/5

sin(b-π/6）=12/13

cos(b-π/6）=5/13

所以

f(a-b)=sin[(a-π/6)-(b-π/6）]

=sin(a-π/6）cos(b-π/6）-cos(a-π/6）sin(b-π/6）

=3/5*5/13-4/5*12/13

=-13/45