Saturday, March 21, 2009

Trigonometric equations and the CAS calculator

There are lots of ways of solving trigonometric equations on the Classpad but I have avoided using Trisolve as it takes away the thinking aspect of trigonometric equations. Instead I focussed on setting up equations in eActivities with the intent to complement them with the Geometry section later.

eActivities are a great place to store frequently used equations. In this instance, I wanted to keep all of the trigonometric and circle equations in one place ie sine, cosine & tan ratios, sine rule, cosine rule, sector, segment equations, circumference, area.

To do this I opened an eActivity from the main menu.

Then I started a new eActivity by going File -> New. Then I saved it by going File->Save. I called it Trig Formulae.

So then I inserted a Numsolve strip to hold my equation.

Once the strip was added I used the soft keyboard to name it the Sine ratio. Then I pressed solve to put the equation in.

Using the mth tab in the soft keyboard and then selecting the Trig option at the base of the soft keyboard I entered 'sin('. Directly below the mth tab, the theta button can be found and then closed the bracket. Don't type the word 's' 'i' 'n' using the soft keyboard as it won't work - it will treat it as s x i x n.

Then using the 2D tab, I created a fraction and using the var option entered o ÷ h. I hit exe, then closed the equation using the x at the top left hand corner of the window.

I then tried it out using the example opp=7, hyp=14, theta = ? I left theta blank, made sure the angle was selected (with the dot next to it coloured in) and pressed solve in the toolbar. Viola, theta = 30°. If you get some weird answers check that the calculator is set in degrees mode. If the answer is still weird, reset the calculator and it seems to work.

Update (25/3/09): After using this with the class for a few days (especially with radians) I noticed a few strange results where the calculator would return unexpected answers (eg for the above example -330°). To fix this, set the Lower bound to 0 and the upper bound to 180 (for degrees) or pi/3.14159 (for radians) and the results will appear as expected.
I then set about putting in the cosine ratio.

It's a great tool for things like the cosine rule where students find it hard to transpose equations and forget negative signs or for circle, segment and sector equations that are commonly forgotten.

Here is a link to other CAS calculator posts.


  1. A major criticism of graphing calculators by school teachers is their ability to store large amounts of text in the same memory that is used to store programs. Such a feature presents a potential for students to cheat on examinations by storing notes and solutions on their calculators.

  2. The criticism is valid and I can understand why Physics and Chemistry have stopped using programmable calculators in their courses. Maths took a different tack in WA (rightly or wrongly) by having a calculator and non-calculator section in exams. This allows a section which focuses on recall/manual calculation and another that focuses on application. I think the jury is out on whether this has watered down the course further post graphics calculator or not.

    It certainly makes certain parts of the curriculum easier to teach as concepts are much easier to demonstrate and experience (graphing, investigating functions and sequences immediately spring to mind).



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