Trigonometric Graphs

New Zealand

Level 7 - NCEA Level 2

Consider the functions $f\left(x\right)=\sin x$`f`(`x`)=`s``i``n``x` and $g\left(x\right)=\sin5x$`g`(`x`)=`s``i``n`5`x`.

a

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

b

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

$x$x |
$0^\circ$0° | $18^\circ$18° | $36^\circ$36° | $54^\circ$54° | $72^\circ$72° | $90^\circ$90° | $108^\circ$108° | $126^\circ$126° | $144^\circ$144° |
---|---|---|---|---|---|---|---|---|---|

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

c

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

d

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

Horizontal dilation by a factor of $5$5.

A

Horizontal dilation by a factor of $\frac{1}{5}$15.

B

Vertical dilation by a factor of $5$5.

C

Vertical dilation by a factor of $\frac{1}{5}$15.

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 6 minutes

Consider the functions $f\left(x\right)=\cos x$`f`(`x`)=`c``o``s``x` and $g\left(x\right)=\cos4x$`g`(`x`)=`c``o``s`4`x`.

Consider the function $f\left(x\right)=\cos x$`f`(`x`)=`c``o``s``x` and $g\left(x\right)=\cos\left(\frac{x}{2}\right)$`g`(`x`)=`c``o``s`(`x`2).

The functions $f\left(x\right)$`f`(`x`) and $g\left(x\right)=f\left(kx\right)$`g`(`x`)=`f`(`k``x`) have been graphed on the same set of axes, in grey and black respectively.

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