Trigonometric Graphs

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

Period changes for sine and cosine

Consider the functions $f\left(x\right)=\sin x$`f`(`x`)=`s``i``n``x` and $g\left(x\right)=\sin3x$`g`(`x`)=`s``i``n`3`x`.

a

State the period of $f\left(x\right)$`f`(`x`) in radians.

b

Complete the table of values for $g\left(x\right)$`g`(`x`).

$x$x |
$0$0 | $\frac{\pi}{6}$π6 | $\frac{\pi}{3}$π3 | $\frac{\pi}{2}$π2 | $\frac{2\pi}{3}$2π3 | $\frac{5\pi}{6}$5π6 | $\pi$π | $\frac{7\pi}{6}$7π6 | $\frac{4\pi}{3}$4π3 |
---|---|---|---|---|---|---|---|---|---|

$g\left(x\right)$g(x) |
$\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |

c

State the period of $g\left(x\right)$`g`(`x`) in radians.

d

What transformation of the graph of $f\left(x\right)$`f`(`x`) results in the graph of $g\left(x\right)$`g`(`x`)?

Vertical dilation by a factor of $\frac{1}{3}$13

A

Vertical dilation by a factor of $3$3

B

Horizontal dilation by a factor of $\frac{1}{3}$13

C

Horizontal dilation by a factor of $3$3

D

Vertical dilation by a factor of $\frac{1}{3}$13

A

Vertical dilation by a factor of $3$3

B

Horizontal dilation by a factor of $\frac{1}{3}$13

C

Horizontal dilation by a factor of $3$3

D

e

The graph of $f\left(x\right)$`f`(`x`) has been provided below.

By moving the points, graph $g\left(x\right)$`g`(`x`).

Loading Graph...

Easy

Approx 8 minutes

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