NZ Level 7 (NZC) Level 2 (NCEA)
Period changes for sine and cosine

## Interactive practice questions

Consider the functions $f\left(x\right)=\sin x$f(x)=sinx and $g\left(x\right)=\sin5x$g(x)=sin5x.

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

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).

Easy
Approx 6 minutes

Consider the functions $f\left(x\right)=\cos x$f(x)=cosx and $g\left(x\right)=\cos4x$g(x)=cos4x.

Consider the function $f\left(x\right)=\cos x$f(x)=cosx and $g\left(x\right)=\cos\left(\frac{x}{2}\right)$g(x)=cos(x2).

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

### Outcomes

#### M7-2

Display the graphs of linear and non-linear functions and connect the structure of the functions with their graphs

#### 91257

Apply graphical methods in solving problems