Find the period and the shift for the function $y = 2 \cot ( 3 x - \pi / 2 )$
A) $\text { period: } \pi / 3 \text {, shift: } \pi / 6 \text { to the right }$
B) $\text { period: } 2 \pi / 3 \text {, shift: } \pi / 6 \text { to the right }$
C) $\text { period: } \pi / 3 \text {, shift: } \pi / 2 \text { to the left }$
D) $\text { period: } 3 \pi \text {, shift: } 3 \pi / 2 \text { to the right }$
E) $\text { period: } \pi / 3 \text {, shift: } \pi / 6 \text { to the left }$

Question

Quizplus · Accepted Answer

The period of a cotangent function $y = \cot(bx - c)$ is $\pi / |b|$, so here it's $\pi / 3$. The phase shift is calculated as $c / b$, which gives $\pi / 2 / 3 = \pi / 6$ to the right, because the equation can be rewritten as $y = 2 \cot(3(x - \pi / 6))$.

Find the Period and the Shift for the Function y=2cot⁡(3x−π/2)y = 2 \cot ( 3 x - \pi / 2 )y=2cot(3x−π/2)

Find the Period and the Shift for the Function $y = 2 \cot ( 3 x - \pi / 2 )$