Graph y= 2cot(2x-pi/2)
State the period and phase shift.
I'll skip the graphing part. Note that
$\displaystyle y = 2\cot \left(2x-\frac{\pi}{2}\right) = 2\cot \left(2\left(x-\frac{\pi}{4}\right)\right)$.
The basic form of the cotangent function is $\displaystyle y = a\cot (b(x - h)) + k$. The period would be $\displaystyle \frac{\pi}{|b|}$, and the phase shift is h.
Therefore, in your problem, the period would be $\displaystyle \frac{\pi}{2}$ and the phase shift would be $\displaystyle \frac{\pi}{4}$.
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