This is the question from my textbook:
The correct answer for the coordinates of $A$ is $\left(\frac{2\pi}{3},\frac{3}{2}\right)$. I've tried making three equations and solving by substitution for $k$ and $c$, but I do not get the correct values. Here's the equations I made:
$0=sin(\frac{4\pi}{3})+c$
$0=sin(\frac{2\pi}{3})+c$
$0=sin(2\pi)+c$
Correct value for $k$ is $\frac{\pi}{6}$, for $c$ it is $\frac{1}{2}$.
Help would be greatly appreciated. Thank you.
Best Answer
hint
from the graph, we derive that
$$f (0)=f (4\frac \pi 3)=0$$
thus
$$\sin (-k)+c=\sin (4\frac \pi 3-k)+c=0$$
from here, $$-k=\pi-(4\frac \pi 3-k) $$
You can finish.