New Zealand
Level 8 - NCEA Level 3

# Key features of cot, sec and cosec curves

## Interactive practice questions

Consider the graph of $y=\sin x$y=sinx for $-2\pi\le x\le2\pi$2πx2π.

a

Complete the table of values, giving your answers correct to three decimal places.

 $x$x $\csc x$cscx $-\frac{2\pi}{3}$−2π3​ $-\frac{\pi}{2}$−π2​ $-\frac{\pi}{4}$−π4​ $\frac{\pi}{3}$π3​ $\frac{\pi}{2}$π2​ $\frac{3\pi}{4}$3π4​ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
b

What would be the asymptotes of $y=\csc x$y=cscx in $-2\pi\le x\le2\pi$2πx2π? That is, where would $y=\csc x$y=cscx be undefined?

Write all values of $x$x on the same line, separated by a comma.

c

At what values of $x$x is $\csc x=1$cscx=1?

Write all values of $x$x on the same line, separated by a comma.

d

At what values of $x$x is $\csc x=-1$cscx=1?

Write all values of $x$x on the same line, separated by a comma.

e

What would be the period of $y=\csc x$y=cscx?

Easy
Approx 9 minutes

Consider the graph of $y=\cos x$y=cosx for $-2\pi\le x\le2\pi$2πx2π.

Consider the graph of $y=\tan x$y=tanx for $-2\pi\le x\le2\pi$2πx2π.

Consider the following pairs of functions and their reciprocals.

### Outcomes

#### M8-2

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