SAT1000 - P321

Geometry

Given the function $f(x)=\sin(\omega x + \dfrac{\pi}{3})\ (\omega>0)$ , $f(\dfrac{\pi}{6})=f(\dfrac{\pi}{3})$ .

If $f(x)$ has minimum value but no maximum value on the interval $(\dfrac{\pi}{6},\dfrac{\pi}{3})$ , then find the value of $\omega$ .

If $\omega=\dfrac{a}{b}$ , where $a,b$ are positive coprime integers. submit $a+b$ .

Have a look at my problem set: SAT 1000 problems