How to Make Trigonometric Ratios Table Working Model

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Here’s how to create a Trigonometric Ratios Table Working Model using cardboard, color paper, and a rotating mechanism. This model will visually display the trigonometric ratios in an interactive way.

Concept:

The model demonstrates the trigonometric ratios (sin⁡θ\sin \thetasinθ, cos⁡θ\cos \thetacosθ, tan⁡θ\tan \thetatanθ, csc⁡θ\csc \thetacscθ, sec⁡θ\sec \thetasecθ, cot⁡θ\cot \thetacotθ) for standard angles (0°, 30°, 45°, 60°, and 90°) in a rotating disk format. Users can rotate the disk to align the angle with its corresponding values.

Materials Needed:

  1. Cardboard: For the base and rotating disks.
  2. Colored Paper: To decorate and label the model.
  3. Push Pin: For the rotating mechanism.
  4. Glue or Tape: To assemble the model.
  5. Marker/Pens: For writing the ratios and values.
  6. Ruler and Compass: For precision in drawing circles.

Step-by-Step Instructions:

1. Create the Base:

  • Cut a square or circular base out of cardboard (around 12 x 12 inches or 12 inches in diameter).
  • Cover it with colored paper for decoration.
  • Label the base with the title: “Trigonometric Ratios Table”.

2. Prepare the Rotating Disks:

  • Cut two circular disks from cardboard:
    • Large disk (approx. 10 inches in diameter): This will display the trigonometric ratios.
    • Small disk (approx. 6 inches in diameter): This will display the standard angles.

3. Divide the Disks:

  • Large Disk:
    • Divide it into 6 equal sections using a ruler and compass.
    • Label each section with one trigonometric ratio: sin⁡θ\sin \thetasinθ, cos⁡θ\cos \thetacosθ, tan⁡θ\tan \thetatanθ, csc⁡θ\csc \thetacscθ, sec⁡θ\sec \thetasecθ, and cot⁡θ\cot \thetacotθ.
  • Small Disk:
    • Divide it into 5 equal sections to represent the standard angles: 0°, 30°, 45°, 60°, and 90°.
    • Write these angles in their respective sections.

4. Write the Trigonometric Values:

  • On the Large Disk, under each ratio section, write the corresponding values for the angles:
    • Example for sin⁡θ\sin \thetasinθ:
      • 0°: 0
      • 30°: 1/2
      • 45°: 1/21/\sqrt{2}1/2​
      • 60°: 3/2\sqrt{3}/23​/2
      • 90°: 1
    • Repeat this for all other ratios (cos⁡\coscos, tan⁡\tantan, etc.).

5. Assemble the Rotating Mechanism:

  • Stack the small disk on top of the large disk.
  • Use a push pin through the center of both disks and into the base. Ensure the disks can rotate freely.

6. Add Labels and Indicators:

  • Add a small arrow or indicator on the small disk to point to one angle at a time.
  • Add a stationary arrow on the base to indicate which trigonometric ratio is being referenced.

7. Decorate the Model:

  • Use colored paper to make the disks visually appealing.
  • Add borders, patterns, or other designs to enhance the look.

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