Drawing Sine and Cosine Functions by Learning & Knowledge
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Drawing sine and cosine functions Hello everyone out there, this tutorial is about drawing or sketching sine and cosine functions without any other tools, including a calculator. You might need one if you have to solve trigonometric equations, for example, or simply because your maths teacher wants you to. With a bit of practice, it's not difficult. I'll give a few examples, comment on the whole thing and explain what's important. This is what you need to know beforehand: You should have the basic form of the sine and cosine functions more or less in your head. If necessary, you can also take a look at the formula collection. Terms such as period and amplitude should be fairly clear; this is explained again in the video. Here is the basic form of the sine function, or simply: the sine. Its center line is the x-axis, so it is neither shifted up nor down. The sine goes through the origin. The basic form of the sine has an amplitude of 1. You can read this off in the diagram, but even if you didn't have the diagram you could still tell from the function equation by reading the number in front of the sine. There's nothing there, you say, and if there's nothing there then you can just write down a 1, that won't change anything. Now for the period. Periodic processes are repeating processes. Here is a high point. It repeats itself here, and here, and so on. The function has an infinite number of such high points, and they are always the same distance apart. This distance is the period, or period length. In the basic form of the sine this is 2Pi, or about 6.3. The high points therefore always repeat after 2Pi. The same applies, of course, to the low points of the function. Let's assume you only have the function equation and no diagram, and you still want to know what period the function has. This is very easy to find out: The formula for this is 2pi divided by the number in front of the x. You say: there is no number there? If that is the case, there is a 1, so the formula is used: 2pi divided by 1, so the period would be 2 pi. If there was a two in front of the x, as in green here, the period would be 2 pi divided by 2, i.e. pi. Here is the basic form of the cosine function, or simply the cosine. The amplitude is 1 as with sine, the period is 2 pi as with sine...
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