Trigonometric Graphs

Consider the equation $y=\sin x$`y`=`s``i``n``x`.

a

Using the fact that $\sin\frac{\pi}{6}=\frac{1}{2}$`s``i``n`π6=12, what is the value of $\sin\frac{5\pi}{6}$`s``i``n`5π6?

b

Using the fact that $\sin\frac{\pi}{6}=\frac{1}{2}$`s``i``n`π6=12, what is the value of $\sin\frac{7\pi}{6}$`s``i``n`7π6?

c

Using the fact that $\sin\frac{\pi}{6}=\frac{1}{2}$`s``i``n`π6=12, what is the value of $\sin\frac{11\pi}{6}$`s``i``n`11π6?

d

Complete the table of values. Give your answers in exact form.

$x$x |
$0$0 | $\frac{\pi}{6}$π6 | $\frac{\pi}{2}$π2 | $\frac{5\pi}{6}$5π6 | $\pi$π | $\frac{7\pi}{6}$7π6 | $\frac{3\pi}{2}$3π2 | $\frac{11\pi}{6}$11π6 | $2\pi$2π |
---|---|---|---|---|---|---|---|---|---|

$\sin x$sinx |
$\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |

e

Draw the graph of $y=\sin x$`y`=`s``i``n``x`.

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Easy

Approx 6 minutes

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