0.5 Phy1020: brief trigonometry tutorial  (Page 13/20)

Very similar code

The code in Listing 7 is very similar to the code in Listing 3 and Listing 5 . The essential differences are that

• Listing 3 uses the sine along with the opposite side and the hypotenuse.
• Listing 5 uses the cosine along with the adjacent side and the hypotenuse.
• Listing 7 uses the tangent along with the opposite side and the adjacent side.

You should be able to work through those differences without further explanation from me.

The cotangent of an angle

There is also something called the cotangent of an angle, which is simply the ratio of the adjacent side to the opposite side. If you know how to work withthe tangent, you don't ordinarily need to use the cotangent, so I won't discuss it further.

Computing length of opposite side with the Google calculator

We could also compute the length of the opposite side using the Google calculator.

Dealing with different quadrants

Up to this point, we have dealt exclusively with angles in the range of 0to 90 degrees (the first quadrant). As long as you stay in the first quadrant, things are relatively straightforward.

As you are probably aware, however, angles can range anywhere from 0 to 360 degrees (or more). Once you begin working with angles that are greater then 90 degrees,things become a little less straightforward.

Another svg file

When you downloaded the zip file named Phy1020.zip using the link given above , you should also have found that the zip file contains a file named Phy1020a1.svg.

The purpose of this file is to make it possible for you to create tactile graphics for sine and cosine curves using the procedure explained in the earliermodule named Manual Creation of Tactile Graphics .

If you have the ability to create tactile graphics, you don't need to perform the work in the following graph board exercise. However, you shouldread about it anyway because that will probably help you to better understand the sine and the cosine of an angle.

I will get back to tactile graphics after I describe the graph board exercise.

Another graph board exercise

In this graph board exercise, we will plot a graph of the amplitude of the sine of an angle on the vertical axis versus the angle itself onthe horizontal.

We will also do the same thing for the cosine. It would be very good if you could plot one curve on the top half of your graph board and the other curve onthe bottom half of your graph board so that you can easily compare the two.

Interpreting gridline values

Since I don't know how many tactile grid lines there are on your graph board, I can't tell you exactly how to interpret the grid lines so as to make maximumuse of the space on the board. All that I can tell you is that the vertical amplitude values for each curve will range from -1.0 to +1.0. We would like toplot values from -360 degrees to + 360 degrees on the horizontal. You should interpret the values of the gridlines on your graph board accordingly.