Key features of cot, sec and cosec curves
Interactive practice questions
Consider the graph of $y=\sin x$y=sinx for $-2\pi\le x\le2\pi$−2π≤x≤2π.
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 | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |
What would be the asymptotes of $y=\csc x$y=cscx in $-2\pi\le x\le2\pi$−2π≤x≤2π? 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.
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.
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.
What would be the period of $y=\csc x$y=cscx?
Consider the graph of $y=\cos x$y=cosx for $-2\pi\le x\le2\pi$−2π≤x≤2π.
Consider the graph of $y=\tan x$y=tanx for $-2\pi\le x\le2\pi$−2π≤x≤2π.
Consider the following pairs of functions and their reciprocals.