已知函数f(x)=sin(x-π/6)+cosx,x∈R.(1)求f(0)的值；(2)当x∈[-π/3,π/2]时,求f(x)的值；(3)若a是第四象限角,且f(a+π/3)=1/3,求tana的值.

Question

已知函数f(x)=sin(x-π/6)+cosx,x∈R.(1)求f(0)的值；(2)当x∈[-π/3,π/2]时,求f(x)的值；(3)若a是第四象限角,且f(a+π/3)=1/3,求tana的值.

Answer 1

(1) f(0)=-1/2+1=1/2
(2) f(x)=sin(x)*sqrt(3)/2-cos(x)/2+cos(x)=sin(x)*sqrt(3)/2+cos(x)/2=sin(x+pi/6)
最大值为1,最小值sqrt(3)/2
(3) f(a+π/3)=sin(a)*cos(pi/6+pi/3)+cos(a)*sin(pi/6+pi/3)=1/3

接触方程即可求出