Graph the function in the ts-plane (t-axis horizontal, s-axis vertical). State the period and symmetry of the function.
-$s=\sec \left(\frac{t}{3}\right)$

A) Period $6 \pi$, symmetric about the s-axis
B) Period $6 \pi$, symmetric about the t-axis
C) $\text { Period } 6 \pi \text {, symmetric about the } t \text {-axis }$
D)$\text { Period } 6 \pi \text {, symmetric about the } s \text {-axis }$

Question

Graph the function in the ts-plane (t-axis horizontal, s-axis vertical). State the period and symmetry of the function.
-$s=\sec \left(\frac{t}{3}\right)$

A) Period $6 \pi$, symmetric about the s-axis 
B) Period $6 \pi$, symmetric about the t-axis 
C) $\text { Period } 6 \pi \text {, symmetric about the } t \text {-axis }$ 
D)$\text { Period } 6 \pi \text {, symmetric about the } s \text {-axis }$

Quizplus · Accepted Answer

The function is periodic with period $6\pi$ because $\sec(\frac{t}{3})$ repeats every $2\pi$ in $t$, which corresponds to a horizontal distance of $6\pi$. The function is symmetric about the $s$-axis because $\sec$ is an even function, meaning that $\sec(-x) = \sec(x)$ for all $x$. Therefore, $\sec(\frac{-t}{3}) = \sec(\frac{t}{3})$ for all $t$, so the graph is symmetric about the $s$-axis.

Graph the Function in the Ts-Plane (T-Axis Horizontal, S-Axis Vertical) s=sec⁡(t3)s=\sec \left(\frac{t}{3}\right)s=sec(3t​)

Graph the Function in the Ts-Plane (T-Axis Horizontal, S-Axis Vertical) $s=\sec \left(\frac{t}{3}\right)$