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.

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

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

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#2:

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

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

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

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#3:

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

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

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

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#4:

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

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

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

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#5:

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

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

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

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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 Graphing f(x)=0.5sec(x + π/2) - 1

$$b)\hspace{.1em}\text{Period:}\hspace{.1em}π$$ $$\text{Phase Shift:}\hspace{.1em}\text{Right}\hspace{.1em}\frac{π}{3}\hspace{.1em}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Up}\hspace{.1em}2$$ Desmos link for more detail Graphing f(x)=0.5sec(2x - 2π/3) + 2

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#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 Graphing f(x)=3sec(x/3 + 7π/4) + 1

$$b)\hspace{.1em}\text{Period:}\hspace{.1em}4π$$ $$\text{Phase Shift:}\hspace{.1em}\text{Left}\hspace{.1em}\frac{2π}{3}\hspace{.1em}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Down}\hspace{.1em}2$$ Desmos link for more detail Graphing f(x)=3sec(x/2 + π/3) - 2

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#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 Graphing f(x)=2sec(x/2 - 3π/4) + 1

$$b)\hspace{.1em}\text{Period:}\hspace{.1em}4π$$ $$\text{Phase Shift:}\hspace{.1em}\text{Left}\hspace{.1em}\frac{π}{3}\hspace{.1em}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Up}\hspace{.1em}1$$ Desmos link for more detail Graphing f(x)=2csc(x/2 + π/6) + 1

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#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 Graphing f(x)=3csc(x/2) + 1

$$b)\hspace{.1em}\text{Period:}\hspace{.1em}π$$ $$\text{Phase Shift:}\hspace{.1em}\text{Left}\hspace{.1em}\frac{π}{4}\hspace{.1em}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Down}\hspace{.1em}2$$ Desmos link for more detail Graphing f(x)=2csc(2x + π/2) - 2

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#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 Graphing f(x)=3csc(x/2 - π/3) - 2

$$b)\hspace{.1em}\text{Period:}\hspace{.1em}π$$ $$\text{Phase Shift:}\hspace{.1em}\text{Left}\hspace{.1em}\frac{π}{12}\hspace{.1em}$$ $$\text{Vertical Shift:}\hspace{.1em}\text{Down}\hspace{.1em}1$$ Desmos link for more detail Graphing f(x)=3csc(2x + π/6) - 1

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