Topics
9. Graphs of Trigonometric Functions
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United States of AmericaUT
Math III

9.05 Graphing secant, cosecant, and cotangent functions

Lesson
Practice

Interactive practice questions

Consider the graph of $y=\csc x$y=cscx. Its first local minimum for $x\ge0$x≥0 is at $\left(\frac{\pi}{2},1\right)$(π2​,1).

By considering the transformation that has taken place, state the coordinates of the first local minimum of each of the given functions for $x\ge0$x≥0.

Loading Graph...
The graph $y=\csc x$y=cscx is plotted on a Coordinate Plane. One period of $\csc x$cscx is shown from $x=0$x=0 to $x=2\pi$x=2π but the graph extends to the left and right. The first local minimum of $y=\csc x$y=cscx is plotted as a solid dot at $\left(\frac{1}{2\pi},1\right)$(12π​,1). The coordinates of the local minimum are not explicitly labeled.

 

a

$y=5\csc x$y=5cscx

b

$y=-5\csc x$y=−5cscx

c

$y=\csc x+2$y=cscx+2

Easy
4min

Consider the graph of $y=\sec x$y=secx. Its first local minimum for $x\ge0$x≥0 is at $\left(0,1\right)$(0,1).

By considering the transformation that has taken place, state the coordinates of the first local minimum of each of the given functions for $x\ge0$x≥0.

Easy
4min

Determine the equation of the new function after performing the following transformations.

Easy
< 1min

Determine the equation of the new function after performing the following transformations.

Easy
< 1min
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Outcomes

III.F.TF.5

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

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