Test Objectives
• Demonstrate the ability to sketch the graphs of secant and cosecant
• Demonstrate the ability to find the period of the secant or cosecant function
• Demonstrate the ability to find the phase shift of the secant or cosecant function
• Demonstrate the ability to find the vertical shift of the secant or cosecant function
Graphing Secant and Cosecant Practice Test:

#1:

Instructions: Find the period, phase shift, and vertical shift. Sketch the graph.

$$a)\hspace{.1em}f(x)=\frac{1}{2}\sec\left(x + \frac{π}{2}\right) - 1$$

$$b)\hspace{.1em}f(x)=\frac{1}{2}\sec\left(2x - \frac{2π}{3}\right) + 2$$

#2:

Instructions: Find the period, phase shift, and vertical shift. Sketch the graph.

$$a)\hspace{.1em}f(x)=3\sec\left(\frac{x}{3}+ \frac{7π}{4}\right) + 1$$

$$b)\hspace{.1em}f(x)=3\sec\left(\frac{x}{2}+ \frac{π}{3}\right) - 2$$

#3:

Instructions: Find the period, phase shift, and vertical shift. Sketch the graph.

$$a)\hspace{.1em}f(x)=2\sec\left(\frac{x}{2}- \frac{3π}{4}\right) + 1$$

$$b)\hspace{.1em}f(x)=2\csc\left(\frac{x}{2}+ \frac{π}{6}\right) + 1$$

#4:

Instructions: Find the period, phase shift, and vertical shift. Sketch the graph.

$$a)\hspace{.1em}f(x)=3\csc\left(\frac{x}{2}\right) + 1$$

$$b)\hspace{.1em}f(x)=2\csc\left(2x + \frac{π}{2}\right) - 2$$

#5:

Instructions: Find the period, phase shift, and vertical shift. Sketch the graph.

$$a)\hspace{.1em}f(x)=3\csc\left(\frac{x}{2}- \frac{π}{3}\right) - 2$$

$$b)\hspace{.1em}f(x)=3\csc\left(2x + \frac{π}{6}\right) - 1$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.1em}\text{Period:}\hspace{.1em}2π$$ $$\text{Phase Shift:}\hspace{.1em}\text{Left}\hspace{.1em}\frac{π}{2}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Down}\hspace{.1em}1$$ Desmos link for more detail

$$b)\hspace{.1em}\text{Period:}\hspace{.1em}π$$ $$\text{Phase Shift:}\hspace{.1em}\text{Right}\hspace{.1em}\frac{π}{3}\hspace{.1em}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Up}\hspace{.1em}2$$ Desmos link for more detail

#2:

Solutions:

$$a)\hspace{.1em}\text{Period:}\hspace{.1em}6π$$ $$\text{Phase Shift:}\hspace{.1em}\text{Left}\hspace{.1em}\frac{21π}{4}\hspace{.1em}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Up}\hspace{.1em}1$$ Desmos link for more detail

$$b)\hspace{.1em}\text{Period:}\hspace{.1em}4π$$ $$\text{Phase Shift:}\hspace{.1em}\text{Left}\hspace{.1em}\frac{2π}{3}\hspace{.1em}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Down}\hspace{.1em}2$$ Desmos link for more detail

#3:

Solutions:

$$a)\hspace{.1em}\text{Period:}\hspace{.1em}4π$$ $$\text{Phase Shift:}\hspace{.1em}\text{Right}\hspace{.1em}\frac{3π}{2}\hspace{.1em}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Up}\hspace{.1em}1$$ Desmos link for more detail

$$b)\hspace{.1em}\text{Period:}\hspace{.1em}4π$$ $$\text{Phase Shift:}\hspace{.1em}\text{Left}\hspace{.1em}\frac{π}{3}\hspace{.1em}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Up}\hspace{.1em}1$$ Desmos link for more detail

#4:

Solutions:

$$a)\hspace{.1em}\text{Period:}\hspace{.1em}4π$$ $$\text{Phase Shift:}\hspace{.1em}\text{None}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Up}\hspace{.1em}1$$ Desmos link for more detail

$$b)\hspace{.1em}\text{Period:}\hspace{.1em}π$$ $$\text{Phase Shift:}\hspace{.1em}\text{Left}\hspace{.1em}\frac{π}{4}\hspace{.1em}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Down}\hspace{.1em}2$$ Desmos link for more detail

#5:

Solutions:

$$a)\hspace{.1em}\text{Period:}\hspace{.1em}4π$$ $$\text{Phase Shift:}\hspace{.1em}\text{Right}\hspace{.1em}\frac{2π}{3}\hspace{.1em}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Down}\hspace{.1em}2$$ Desmos link for more detail

$$b)\hspace{.1em}\text{Period:}\hspace{.1em}π$$ $$\text{Phase Shift:}\hspace{.1em}\text{Left}\hspace{.1em}\frac{π}{12}\hspace{.1em}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Down}\hspace{.1em}1$$ Desmos link for more detail