Sine, cosine, tangent – these terms enter a student’s life when they study trigonometry books in high school. It does require a little bit of rote memorization to be familiar with the trigonometry rules. But, that is not the only way to learn. Learning by activities helps gain practical insight. It is why students prepare projects, do assignments and perform gamified activities. In this post, we bring you a few, very interesting trigonometry activities that are appropriate for the high school curriculum.

**Learning with activities – A practical way to boost conceptual knowledge**

At the high school stage, the students are freshly introduced to complex subjects like trigonometry. Adding a little fun to the learning process helps in a smooth transition. Activities help get that fun factor in the concept-building process. When early trigonometry beginners start feeling overwhelmed by the terms like theta, sine, cosine, tangent, trig. relationships or ratios, etc. they can offload some stress with gamified activities.

Activities can provide a refreshing break from the typical learning procedures. The choice of backdrops, props, and the creative utilization of concept are some engaging factors that leave a profound impact on the learners’ proficiency. The outcomes are longer concept retention and quick retrieval (Research Review, Does Active Learning Work, Michael Prince, 2004, Journal of Engineering Education).

We all have played riddles, created acronyms, and solved puzzles to beat the academic stress. Our list of the trigonometry activities mentioned below can add more to your repertoire of learning materials fit for the high school level.

**Activities for to learn and apply trigonometry principles**

**1. Make graphs on ground** **or chart paper**

Trigonometric functions can be represented on graph paper. This activity employs the ground as graph paper. If it is sand, you use your fingers to draw the relationship. Various concepts like a sine wave, cos wave, and the trigonometric relationships based on these functions become easier to internalize. This activity allows you to rip the concept off the typical graph paper and put it on a more relatable base. Such an approach utilizes your tactile and visual senses together. Another outcome is a deeper interest in exploring principles behind the waves and functions arising from trigonometry concepts.

This activity can be done in pairs. One member can draw the graph and the partner tells the function represented by the wave. It promotes a collaborative approach in learning and enables looking into other ways to establish trigonometry ratios and functions.

**2. Play hand rule trick** **quiz**

This activity is a prompt or a cheat trick that can instantly tell about the values of various trigonometric expressions. In the hand rule trick,

- Starting from little finger to thumb fingers, assign the five angles commonly encountered in early trigonometry.
- Little finger – 0, ring finger – 30, middle finger – 45, index finger – 60, and thumb – 90 degrees.
- Ensure that the palm side is up while assigning.

Now, the trick is the (square root of the number of fingers below the angle finger) / 2 is the value of sine of that angle. Thus, the sine 30 is the square root of 1 divided by 2 = 1/2.

Demonstrate this trick first and then design a quiz based on it. You can play a rapid quiz with friends in a group. A volunteer displays the cue angle by marking it on the finger and the others tell the answer. It can help create a shortcut to calculations and save you a lot of time in exams.

**3. Make a unit circle on a plate**

A unit circle is a handy tool for learning about the relationships peculiar to right-angle triangles. Make this structure on a plate or cardboard sheet and color it. The whole process of designing this unit circle helps learn the relationship between the right-angle triangles’ angles and sides. All angles when imagined inside a unit circle can be represented in the expressions involving π. You must be aware that 1 π = 360^{o}.

This activity is normally done as a project and offers a readymade reference material to remember triangles’ angles and their corresponding π values. It prepares you for solving various problems related to graphing, trigonometric ratios, etc. As a high school student, you can do this activity to learn the basics of trigonometry and construct a strong primer to move further to complex problems.

**4. Play quiz with colored task cards**

Right from preparing task cards to playing quizzes, this activity offers everything required to learn trigonometry basics. The cards prepared may contain simple questions like ‘find the missing angle’ or ‘find the missing side’. Apart from these, sine, cosine, and tangent values in fraction form can also be included in task cards.

Students at the high school level can design a variety of questions like true or false, review the triangle, etc. Participants can employ their mental math capabilities to answer the questions fastest; it is where the challenge lies and makes this activity suitable for learning high school trigonometry.

**5. Play matching game with flashcards**

Students can divide themselves into groups. One group writes the explanations or cues on flashcards. The other group guesses the answer based on the cue. That is how they pair up the cues with answers. The most interesting thing to do with flashcards is to match the graphical representation with the corresponding trigonometric function.

Pythagorean theorem-based equations and the corresponding answers of missing variables in them is the other activity idea that can be used in matching flashcard activity. We can also employ flashcard matching to memorize degrees and corresponding radian values. Flashcards are used for teaching math concepts since primary level; the familiarity factor eases the learning woes for trigonometry students.

**6. Use Base-10 blocks to explain Pythogorean theorem**

Base-10 block is versatile math manipulative. Various concepts like place values, fractions, and basic calculations are taught at the primary level. This manipulative continues to prove its relevance in simplifying the Pythagorean theorem for starters. Take a right-angle triangular block having sides 3cm, 4cm, and 5cm in length. You can create 3×3, 4×4, and 5×5 matrices using base-10 blocks and juxtapose them along the block’s sides. When you count the number of blocks in the matrices, the numbers will come as 9, 16, and 25 respectively. This activity verifies the Pythagoras theorem that stipulates: (base)^{2} + (height)^{2 }= (Hypotenuse)^{2}

It is a simple activity but helps students relate to theory better. Students improve their visualization abilities and may feel comfortable with the idea of applying the theorems in assessing real-life structures.

**Conclusion**

Trigonometry needs to be mastered as it stays with us almost throughout life. The main aim of trigonometry activities is to make the learning process enjoyable and easier for high school students. Since by the way of doing, they indulge themselves deeper into concepts, they find appreciable improvement in their understanding through visualization. Instead of forcing themselves to rote memorize, they act and create readily accessible learning materials, and make trigonometry fun.