函数y=根号(x-4)+根号(15-3x如何用三角函数求值域

y=√(x-4)+√(15-3x)
x-4≥0,15-3x≥0
4≤x≤5
设x-4=sin²t,(0≤t≤π/2)
15-3x=15-3(sin²t+4)=3(1-sin²t)=3cos²t
y=√(sin²t)+√(3cos²t )
=sint+√3cost
=2(1/2sint+√3/2cost)
=2sin(t+π/3)
因为0≤t≤π/2,所以π/3≤t+π/3≤5π/6
1≤2sin(t+π/3)≤2
y的值域为[1,2]