%\addcontentsline{toc}{section}{Activity 3.16}
\section*{Activity 3.16}

To guide learners to draw a proper $\sin$ curve, I will first want them the fill in the following table.\\

\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline $x$ (in Radians)& 0 &0.25& 0.5&0.75 &1 & 1.25& 1.5& 1.75 & 2& ... &$2\times \pi$\\ \hline $y=\sin x$ & &&&&&&&&& &\\ \hline
\end{tabular}\\
%& 2.75& 3&3.5& 4 &4.5 &5 &5.5& 6

\noindent
Once they finish filling in the values of $y$ as many as possible, then they can plot the ordered pairs on a Cartesian plane. The $x$ values should be very close to each other to avoid strait lines from point to point. Joining the points plotted from 0 until $\frac{\pi}{2}$, a curve is going to be formed. Hence, …show more content…
I remember when a learner was requested to draw a graph $y + 2^x = -2$ and then he add $-(2^x)$ both sides, then have an equation like $y = -2^x - 2$. He thinks the base (2) is negative and when he create a table $-2^x$ is positive for every $x$ even and negative if $x$ is odd. That was confusing the child. I ask him to draw a function $y = 2^x + 2$. The learner was able to draw the graph and then I asked him to reflect it along the $x$-axis. Then he tried but fail. So I helped him and the learner was happy about the drawing of the graph $y + 2^x = -2$. The best way learners can understand how the graphs curve is to let them use too many point, but this consume time. If learners can use too many point from $x = 0^{\circ}$ to $x = 90^{\circ}$ and then to $x = 180^{\circ}$ they will notice that from the point $(0^{\circ}; 0)$ to the point $(90^{\circ}; 1)$ is not a straight line but an increasing curve, also they will further notice that from the point $(90^{\circ}; 1)$ to the point $(180^{\circ}; 0)$ is also not a straight line. Using many values of $x$ can also help them to see that $\sin$ function is bounded by 1 and -1 and it is defined for every $x\in