# How do you find the important points to graph  f(x) = 20sin(π/6(t)) + 4?

I used calculus for this: The derivative of that equation is $\frac{20 \pi}{6} \cdot \cos \left(\frac{\pi}{6} t\right)$ The critical points are where the derivative (or slope of the graph) equals zero, You get left with $\cos \left(\frac{\pi}{6} t\right) = 0$. And using the unit circle you find that cos is 0 at $\frac{\pi}{2} + \pi n$ so to get $\frac{\pi}{6} t$ to $\frac{\pi}{2}$, t=3, and then to keep adding pi you keep adding 6, so t=3,9,15,21...