Who said you can't teach Trigonometry outdoors? There are many Trigonometry experiments you can perform outdoors, such as measuring experiments and rocket experiments. Here are a few more experiments:

Giant Unit Circle

The unit circle is a crucial tool in analytic trigonometry. Most of the time, the unit circle is drawn on the board and the angles and their coordinates are plotted on it. Why not give your students free reign and a chance to play with that giant compass and protractor of yours?

1. For this experiment, you'll need an area outside the classroom where your students can draw. You can ask for permission to use the basketball court or the quadrangle.
2. Materials needed include colored chalk, rags (for erasures, of course), a giant compass, protractors and meter sticks.
3. Assign an area for each group to draw on. Ask them to draw the unit circle (diameter of 2 meters). Make sure to check accuracy and neatness of the unit circles.
4. Give a list of angles to be plotted on the circle. Each quadrant must have one angle at the least.
5. Your students will use the protractor to measure the angles relative to the positive x-axis. Once they have plotted the angle up to a point on the unit circle, they must find the x and y (x, y) coordinates of the plotted point. They should use the meter stick to measure the x and y coordinates of each angle.
6. All the measurements should be recorded on your experiment or activity sheet. Format can be: Angle (x coordinate in meters, y coordinate in meters).
7. After all the angles have been plotted and measured, the next step will be to compute for the x and y coordinates using sine and cosine. (x coordinate=sin θ, y coordinate=cos θ)
8. You can provide a table for the side-by-side comparison of the actual measurements of the coordinates and the computed values. Remind them that since the values are plotted on the unit circle, the values of the coordinates should have positive or negative signs.
9. Additional generalizations that can be drawn from the experiment can include which angles have positive x coordinates or positive y coordinates (All Students Take Calculus mnemonic), and the relationships of the coordinates of the angles in the first quadrant with those in the second, third and fourth quadrants (corresponding acute angle concept).

The Human Wave

The Wave for most of sports fans is a move wherein the crowd moves up and down to form a "wave" around or across a stadium. For this experiment, however, the Human Wave is the plotting of the "waves" of the trigonometric functions using, well, your students.

1. For this experiment, you will need straw rope or strings in three different colors, meter stick for measuring, and chalk.
2. Find an area in the school where your students can fit, preferably the basketball court or the school quadrangle. Draw a Cartesian plane and plot the π coordinates on the x and y axes. Make sure your students will have ample space when they stand on the coordinates. (Don't forget to leave a sign that says, "Please do not erase!" You can also surround the area with a police line.)
3. Group your students into three. On the day of the experiment, give each group a roll of string or straw rope. Each group should have a different color of rope or string.
4. Review the unit circle in class before performing the activity.
5. Assign the sine, cosine and tangent functions to the three groups. Note the colors for each.
6. Give each group instructions on how to plot their respective functions on the giant Cartesian plane using the concept of π multiples. You can also make this a challenge to see how well they have mastered the concepts of the circle and the unit circle.
7. After 10 minutes, call the first group (sine group) and ask them to plot the sine wave or sine function graph on the Cartesian plane. The students will be the coordinates and the string or rope will outline the wave.
8. Ask the other groups to note observations on the wave or graph, including the zeroes of the graph and how the graph relates to the unit circle.
9. Repeat the same for the other two groups.
10. For a bonus, ask all three groups to form the waves of their trigonometric functions on the Cartesian plane all at the same time. They should note how the other two waves relate to their own group's wave.
11. For a simple version, you can ask your students to replicate a drawing of the sine, cosine and tangent waves instead of asking them to analyze before plotting.

Triangle Experiments

What is Trigonometry without triangles? After teaching how to solve for the legs and angles of a right triangle, use this experiment as a bridge to solving values for non-right triangles.

1. For this activity, you will need various large triangle cutouts from cartolina or cardboard. The triangles should be right triangles that can be paired up to form non-right or oblique triangles (tangram style). Make four to five sets of these, depending on how many groups you have in class.
2. Distribute the triangles to the groups. The first task for them will be to solve for the legs and angles of the right triangles using the Pythagorean Theorem. The measurements should be recorded on the activity or experiment sheet.
3. The next task for them will be to form obtuse triangles using two of the right triangles. The newly formed triangles will be drawn on the activity sheet.
4. Ask your students to find the measurements of the legs and angles of the obtuse triangles using the measurements of the right triangles. The values will be recorded in a table in the activity sheet.
5. After the measurements for the obtuse triangles have been made, the students will solve for the theoretical measurements of the obtuse triangles using the Sine Law. The computed values will be recorded in a table in the activity sheet.
6. The comparison of the values in the table as well as the triangle formations serves as good introductions to the proof and concept of the Sine Law.

(Many thanks to the creators of TheMathPage.com for the recap on Trigonometry lessons and to the moderators of TeachMaths-InThinking.co.uk for the inspiration. For Trigonometry teaching tools, check out Professor Steven Wilson's materials—cool animated graphs included—at http://staff.jccc.net/swilson/trig/index.htm.)