# How do you graph y=1/3sec((pix)/2+pi/2) and include two full periods?

The first transformation is a vertical shrink by 1/3, you can just multiply the values of the y-axis by 1/3. Second there is a horizontal shrink by 2/$\pi$, you can just multiply the x-axis values by 2/$\pi$. If you solve for $\frac{\pi x}{2} + \frac{\pi}{2} = 0$ You can see that the phase shift is -1 and move the graph to the left one. Since the period of sec is $2 \pi$ you divide that by the coefficient of x to get the new period. $\frac{2 \pi}{\frac{\pi}{2}} = 4$ and you need two periods, so multiply the period by two and graph for 8 along the x-axis.