 New Zealand
Level 8 - NCEA Level 3

Period changes for sine and cosine

Interactive practice questions

Consider the functions $f\left(x\right)=\sin x$f(x)=sinx and $g\left(x\right)=\sin3x$g(x)=sin3x.

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 $g\left(x\right)$g(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​ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
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).

Easy
Approx 8 minutes

Determine whether $\sin2x$sin2x is odd, even, or neither.

Consider the function $y=\sin\left(\frac{x}{4}\right)$y=sin(x4).

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

Outcomes

M8-2

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