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.
State the period of $f\left(x\right)$f(x) in radians.
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) | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |
State the period of $g\left(x\right)$g(x) in radians.
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
Vertical dilation by a factor of $3$3
Horizontal dilation by a factor of $\frac{1}{3}$13
Horizontal dilation by a factor of $3$3
The graph of $f\left(x\right)$f(x) has been provided below.
By moving the points, graph $g\left(x\right)$g(x).
Determine whether $\sin2x$sin2x is an odd function, an even function, 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.