[Math] Drawing sine and cosine waves

Question

I like mathematics and pretty much every mathematical subject, but if there is one thing I thoroughly dislike, it is drawing (functions, waves, diagrams, etc.) We have this important trig test coming up and I need to master the drawing of sine and cosine waves. Can you guys give me an action plan of how to draw (co)sine waves? Like what to do first, second and so on. I missed a month of school because of my pneumonia so I really need all the help I can get (outside of school).

Answer 1

Once you're comfortable with the information in the earlier posts, you can graph more complicated functions of the form $f(x)=a\sin{(b(x-c))}+d$. The parameter $d$ quantifies vertical translation; $a$ is a vertical dilation (amplitude of the wave). The parameter $b$ corresponds to horizontal dilation, whereas $c$ corresponds to horizontal translation.

For example, to graph $f(x) = 3\sin{(2(x-\frac{\pi}{2}))}-1$, you can translate the graph of $y=\sin(x)$ by $\pi/2$ units to the right, then halve its period (double the number of peaks & troughs in an interval of length $2\pi$), stretch that vertically by multiplying every y-coordinate by three, and then translating the whole graph down one unit. I'm too new a user to be able to post a picture, but if you want visualization, you can visit Wolfram Alpha (link)