Can anyone please tell me what is midline and amplitude of the curve $y = 3\csc \left(\frac{\theta}{2} - \frac{\pi}{3}\right)+2.$
My Attempt: As maximum and minimum of $y = 3\csc (\frac{\theta}{2} - \frac{\pi}{3})+2$ do not exist. The amplitude of it will also not exist. $3\csc (\frac{\theta}{2} - \frac{\pi}{3})$ does not exist when $(\frac{\theta}{2} - \frac{\pi}{3}) = 0$. Then how we will find the midline ?
can anyone please help me ?
If you plot the cosecant function, you notice that it consists of repeating intervals of length $\pi$, alternating one above $y=1$, the next below $y=-1$. scaling and shifting $\theta$ will just scale/shift the intervals, but not the amplitude. When you multiply by $3$ you change the amplitude, and then you shift it up by $2$. So the midline will be $y=2$.