$y=2\cos x$, $y=0.5\sin x$, $y=4\cos x$, $y=2\sin x$ when graphed chose which of the function intersect x-axis at $\left({180}^{\circ },0\right)$ and $\left({360}^{\circ },0\right)$.

sketch the graphs of the functions $y=\cos x, y=\cos 2x$ and $y=\cos \frac{1}{2}x$ for $0\le x\le 360°$. Check with your GDC or with dynamic geometry software.

Add the graph of $y=2\cos 2x$ to your sketch.

sketch the graphs of the functions $y=\cos x, y=\cos 2x$ and $y=\cos \frac{1}{2}x$ for $0\le x\le 360°$. Check with your GDC or with dynamic geometry software.

Add the graph of $y=2\cos 2x$ to your sketch.

Write down the amplitude and period of each graph, in a table like this:

$\begin{array}{|cccc|}\hline \text{ Graph }& y=\cos x& y=\cos 2x& y=2\cos 2x\\ \text{ Period }& & & \\ \hline\end{array}$

Predict how the graph of $y=\cos x$ changes when it is transformed to $y=\cos \frac{1}{2}x$. Predict the period of the graph of $y=\cos \frac{1}{2}x$. Check with your GDC or geometry software.

sketch the graphs of the functions $y=\cos x, y=\cos 2x$ and $y=\cos \frac{1}{2}x$ for $0\le x\le 360°$. Check with your GDC or with dynamic geometry software.

Add the graph of $y=2\cos 2x$ to your sketch.

Write down the amplitude and period of each graph, in a table like this:

$\begin{array}{|cccc|}\hline \text{ Graph }& y=\cos x& y=\cos 2x& y=2\cos 2x\\ \text{ Period }& & & \\ \hline\end{array}$

Predict how the graph of $y=\cos x$ changes when it is transformed to $y=\cos \frac{1}{2}x$. Predict the period of the graph of $y=\cos \frac{1}{2}x$. Check with your GDC or geometry software.

Add a column for $y=\cos \frac{1}{2}x$ to your table.