Topics
Trig Graphs (rad)
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CanadaON
Grade 12

Mixed transformations of cot, sec and cosec curves and equations

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 Cartesian 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

12F.B.2.3

Graph, with technology and using the primary trigonometric functions, the reciprocal trigonometric functions for angle measures expressed in radians, determine and describe key properties of the reciprocal functions, and recognize notations used to represent the reciprocal functions

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