(1)过C点作CE⊥AB于E点,则在Rt△BEC中,CE=BCsinB=BCsinx=2√3sinx.
在Rt△AEC中,AC=CE/sinA=2√3sinx/(√3/2)=4sinx.
sinC=sin(A+x).
AB/sinC=BC/sinA.
AB=2√3sinC/(√3/2)=4sinC.=4sin(A+x)=4sin(60°+x)
y=AB+CA+BC
=4sin(60°+x)+4sinx+2√3
=4[sin(60°+x)+sinx]+2√3.
=4*{[2sin(60°+x+x)/2]*cos(60°+x-x)/2}+2√3.
=8*sin(30°+x)cos30°+2√3.
∴y=4√3sin(30°+x)+2√3.----(1)所求函数y=f(x)的解析式;
f(x)的定义域为:0