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Trigonometric function of high school liberal arts mathematics problems
Solution: (1) expand sin(x+π/6) to get f(X)= (radical number 3)/2sinxcox+1/2cosxcosx-1.

= (radical number 3)/4sin2x+1/4cos2x-3/4 =1/2 ((radical number 3)/2sin2x+1/2cos2x)-3/4 =1/.

So the minimum positive period T=2π/2=π.

(2) Because -π/6

So -π/3

Draw the image of Sinks,

So the minimum value =- 1, and the maximum value =- 1/4.