a-maths!

(a)若y=asin(4x+π/6)+b,其中a,b為常數,試求a和b的值。
y=cos(2x-π/12)sin(2x+π/4)。
y=0.5[sin(4x+2π/12) - sin(-4π/12)]
=0.5sin(4x+π/6)+√3
comparing the coefficient,
a=0.5, b=√3

(b)試求y的極大值和極小值。
-1≦sin(4x+π/6)≦1
-0.5≦0.5sin(4x+π/6)≦0.5
-0.5+√3≦0.5sin(4x+π/6)+√3≦0.5+√3
-0.5+√3≦y≦0.5+√3

the max. value is 0.5+√3
the min. value is -0.5+√3