Lab 2:  Computing Values of Trigonometric Functions

    Below is a figure in which a right triangle ABC has the positions of points A and B adjustable.  You can drag the points A and B and see how the reported measure of the angle size and the lengths of the sides of the triangle vary.  Experiment with the figure to answer the questions on the WebCT form.  You should work with a partner to get and give help, but each of you should submit your own WebCT answers. 

Click here to open a WebCT window.   Log on to myWebCT using your WVU email name (without the @wvu.edu extension) as your User Name and the last 4 digits of your student number as your Password.  If you don't know your WVU email name you can find it here.  Answer the questions in Lab 2.  After you complete the lab you can submit your answers and review the correct answers to make sure you understand. 


Sorry, this page requires a Java-compatible web browser.

If you lose any of the points as you drag them around, hit the Refresh button of this window of the web browser to redraw the figures.  The refresh button looks like this in Internet Explorer: .  It is called Reload in Netscape and looks like this: .

For calculations, you can use your own calculator or the Windows calculator.  Open the Windows calculator from the Start menu via Start ® Programs ® Accessories.  You can View the Scientific version of the calculator to access trigonometric functions.


Answer the following questions in WebCT:

1.  The initial measure of angle CBA is 33.516oUse the lengths of sides in the figure to calculate csc(33.516o).  Report your answer correct to 3 decimal places.

2.  How long is the hypotenuse of an isoceles right triangle whose sides are of length 228 units?  Answer correct to 3 decimal places.

3.  Suppose we want the measure in degrees of the smallest angle in a 3-4-5 right triangle.  The units in the figure are too small to make a picture at that scale easy to interpret.  Figure out a way to use similar triangles in the figure so you can view this angle in a triangle that fills a large part of the figure's viewing area.  Report the angle correct to 2 decimal places.

4.-5.  "Solving" a right triangle involves giving all angle measures and side lengths, once you are given some partial information.  Eventually we will learn how to solve an arbitrary triangle analytically, but with the figure above you can recover missing information for the right triangle directly.   Adjust the figure to find the length of the hypotenuse if AC (side b in the figure) is 223 units and angle CBA is 37.559o.   Also find the measure of the other acute angle in degrees.  Report both answers correct to as many decimal places as the figure provides.

6.-7.  So far we have only defined trigonometric functions for acute angles, angles whose measure is greater than 0o and less than 90o.  Let us consider trigonometric functions of 90o angles as limiting cases of acute angles.  Refresh the display, then move point A so that angle CBA gets larger and larger, approaching 90o.  What happens to the relative sizes of sides b and c? What value should we assign to sin(90o)?

8.  How about the tangent of 90o?  What problem arises with the ratio defining the tangent function when angle CBA gets larger and larger, approaching 90o?

9.  Study limiting ratios in the figure to decide what value should be assigned to sec(0o).

The last two questions do not involve the figure, but you will need to use the Windows calculator or another scientific calculator.

10.-11.  Besides degrees and radians, another measure of angle size that is sometimes used is the grad.  Scientific calculators often allow you to specify deg, rad, or grad as a mode for doing trigonometric calculations.  Perform the following experiment:  Pick a convenient angle in degrees (say 45) and calculate sin().  Now set the calculator to grad mode and find the grad angle measure that gives the same value of the sin function.  What grad measure of the angle works to give a matching value of the sin function?  Scale your answer up to decide how many grads there are in a complete revolution, corresponding to 360o or 2 radians.     


Don't forget to submit all your WebCT answers when you are done.  You can access this lab later from any computer with an internet connection and a java enabled browser, in case you want to work through it again.  Browse to it from my home page, at the address handed out on the course syllabus.