Trigonometry is one of the essential branches of mathematics that deal with the measurement of angles, their relationships, and their applications. The understanding of trigonometry is essential for science, engineering, and mathematics courses. In trigonometry, there are six fundamental functions, known as trigonometric ratios, sine, cosine, tangent, cosecant, secant, and cotangent. In this article, we will focus on activities that will teach students to find trigonometric ratios using reference angles.

**Understanding Reference Angles in Trigonometry**

Reference angles are essential in trigonometry as they help students find the trigonometric ratios of any angle. The reference angle is the acute angle formed by the terminal side of an angle and the x-axis. To find the reference angle, subtract the angle from a complete 360-degree circle, and then determine which quadrant the angle is in. Once students understand the concept of reference angles, they are ready to learn how to use them to find trigonometric ratios.

**Activity 1: Using reference angles to find sin and cos ratios**

Materials: Protractor, paper, and pencil

Instructions:

1. Provide students with a list of angles, including those in the first quadrant (0-90 degrees), second quadrant (90-180 degrees), third quadrant (180-270 degrees), and fourth quadrant (270-360 degrees).

2. Ask students to draw each angle on the paper using a protractor.

3. On the same paper, ask students to draw a complete 360-degree circle.

4. Ask students to identify the reference angle for each angle.

5. Using the reference angle, ask students to find the sine and cosine ratios of each angle.

6. Discuss the results and solution methods with the class.

**Activity 2: Using reference angles to find tangent ratios**

Materials: Protractor, paper, and pencil

Instructions:

1. Provide students with a list of angles, including those in the first quadrant (0-90 degrees), second quadrant (90-180 degrees), third quadrant (180-270 degrees), and fourth quadrant (270-360 degrees).

2. Ask students to draw each angle on the paper using a protractor.

3. On the same paper, ask students to draw a complete 360-degree circle.

4. Ask students to identify the reference angle for each angle.

5. Using the reference angle, ask students to find the tangent ratio of each angle.

6. Discuss the results and solution methods with the class.

Activity 3: Using reference angles to find all trigonometric ratios

Materials: Protractor, paper, and pencil

Instructions:

1. Provide students with a list of angles, including those in the first quadrant (0-90 degrees), second quadrant (90-180 degrees), third quadrant (180-270 degrees), and fourth quadrant (270-360 degrees).

2. Ask students to draw each angle on the paper using a protractor.

3. On the same paper, ask students to draw a complete 360-degree circle.

4. Ask students to identify the reference angle for each angle.

5. Using the reference angle, ask students to find the sine, cosine, tangent, cosecant, secant, and cotangent ratios of each angle.

6. Discuss the results and solution methods with the class.

**Conclusion**

Finding trigonometric ratios using reference angles is fundamental in trigonometry. The above activities will help students understand reference angles and their use in finding trigonometric ratios, which will provide a solid foundation for further study. Teachers can modify these activities to suit various teaching needs, including collaborative activities and incorporating technology in the learning process.