Evaluating Trig Functions Tarsia Puzzle

Give your students plenty of practice evaluating trig functions with this fun tarsia puzzle. In this activity, students must use either their knowledge of special right triangles or the unit circle in order to evaluate each function and match the corresponding pieces to build a triangle.

For years, I tried to use a similar evaluating trig functions square puzzle from NCTM, but my students would often end up frustrated because there were many repeated answers throughout the puzzle.

As a result of these repeated answers, the puzzle because much more of a mega complicated logical reasoning/puzzle solving activity instead of a math practice activity.

I decided this was the year I was going to finally make my own matching puzzle for evaluating trig functions.

Required Knowledge

I used this activity with my precalculus students when they were evaluating trig functions by drawing the angle on the coordinate plane in standard position and constructing the appropriate special right triangle.

Students will need to know:

• knowledge of sine, cosine, tangent, cosecant, secant, and cotangent
• how to sketch angles in standard position in either degrees or radians
• how to sketch negative angles in standard position
• side lengths of special right triangles
• determining the sign of a trig function based on its quadrant of the coordinate plane
• evaluating a trig function from a diagram on the coordinate plane
• evaluate a trig function of a quadrantal angle – make sure you have taught this topic or students will be quite confused! A quadrantal angle is an angle which lies on either the x-axis or y-axis when sketched in standard position. An example of this would be finding sin(180 degrees).

I had my students use small dry erase boards to draw each angle/triangle on the coordinate plane.

Alternatively, you could also use this evaluating trig functions puzzle as a practice activity for evaluating trig functions using the unit circle.

In fact, you could likely use this activity for evaluating trig functions without the unit circle and again later in the unit for evaluating trig functions with the unit circle. I doubt students would even notice that it was the exact same set of questions!

Two Versions of Activity: Degrees and Radians

I have created two different versions of this evaluating trig functions activity. Both versions share the exact same questions, but one version features angles in degrees while the other version features angles in radians.

Printing Instructions

The tarsia puzzle will print on two letter-sized sheets of paper. The resulting triangles are quite large, and they are perfectly sized for students working together in groups.

If you would like to print smaller individual puzzles so that each student has their own copy, you could change your PDF settings to print 2 pages on one letter-sized sheet of paper.

Not in the US? You should be able to easily scale the PDF pages to print on A4 paper or print both pages on a single A4 sized sheet of paper for smaller puzzle pieces.

Prepping the Activity

I printed several sets of the tarsia puzzle pieces. I wanted the larger triangles since I have my students working together at tables.

I printed each set of pieces off on a different color of paper so that I can easily find which bag a missing piece belongs in if it happens to land on the floor. I learned this trick at a workshop years ago, and it has been a true classroom lifesaver!

Since my students work together in groups and I want to be able to reuse the activity across my 3 different sections of precalculus and from year to year, I laminate all of my tarsia puzzles and similar activities.

I know that some teachers prefer to skip the lamination and have students cut out the pieces, assemble the tarsia puzzle, and glue the resulting puzzle to a piece of large paper.

Cut out the individual pieces. If you skipping the lamination route, you could definitely give this job of cutting out the pieces to the students to do.

I put each set of tarsia puzzle pieces in a snack sized ziplock bag for easy storage and distribution to students.

Puzzle Instructions

Because I have done so many activities like this with my students in the past, I didn’t really have to give them instructions. I just passed out the bags of triangle puzzle pieces to each group of students, and they immediately got to work.

If students need more guidance, tell them to lay out all of the puzzle pieces on their desk with the printed side facing up.

Choose one of the triangles that has a trig function to evaluate. Work out this value using whatever method you taught (drawing a diagram or using the unit circle).

Then, they should be able to find that answer on another triangle. They can now put these two triangle pieces together so that the question and the answer are next to one another.

If all of the trig functions are evaluated correctly, it should form a large triangle.

Creating Your Own Tarsia Puzzles

Want to create your own tarsia matching puzzle? I created this puzzle using the Formulator Tarsia software from Hermitech Laboratory.

The software looks quite dated, but it is free and it’s pretty easy to figure out how to work.

If you don’t need to type any math symbols, it might be worth checking out this online Tarsia Maker website.