Trigonometric Graphs

Consider the graph of $y=\sin x$`y`=`s``i``n``x` for $-2\pi\le x\le2\pi$−2π≤`x`≤2π.

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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`=`c``s``c``x` in $-2\pi\le x\le2\pi$−2π≤`x`≤2π? That is, where would $y=\csc x$`y`=`c``s``c``x` be undefined?

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

c

At what values of $x$`x` is $\csc x=1$`c``s``c``x`=1?

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

d

At what values of $x$`x` is $\csc x=-1$`c``s``c``x`=−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`=`c``s``c``x`?

Easy

Approx 9 minutes

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