New Zealand
Level 8 - NCEA Level 3

# Transformations of cot, sec and cosec curves and equations

## Interactive practice questions

Consider the graph of $y=\csc x$y=cscx. Its first local minimum for $x\ge0$x0 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 $x\ge0$x0.

a

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

b

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

c

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

Easy
Approx 4 minutes

Consider the graph of $y=\sec x$y=secx. Its first local minimum for $x\ge0$x0 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 $x\ge0$x0.

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

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

### Outcomes

#### M8-2

Display and interpret the graphs of functions with the graphs of their inverse and/or reciprocal functions