NZ Level 8 (NZC) Level 3 (NCEA) [In development]
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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.

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a

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

$x$x $-\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
$\csc x$cscx $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
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
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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

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