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.
State the period of $f\left(x\right)$f(x) in degrees.
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) | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |
State the period of $g\left(x\right)$g(x)in degrees.
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.
Horizontal dilation by a factor of $\frac{1}{5}$15.
Vertical dilation by a factor of $5$5.
Vertical dilation by a factor of $\frac{1}{5}$15.
The graph of $f\left(x\right)$f(x) has been provided below.
By moving the points, graph $g\left(x\right)$g(x).
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