Mathematics Classroom Activity - Class 11 Mathematics Topic: Trigonometric ratios of Quadrantal angles

 Mathematics Classroom Activity

Class 11 Mathematics

Topic: Trigonometric ratios of Quadrantal angles

Objective:

How trigonometric function values are determined for a Quadrantal angles

Materials Required:

• Graph sheet
• Compass
• Protractor
• Ruler
• Pencil

Step-by-Step Activity:

1. Draw the Unit Circle:

• Take a graph sheet and mark the x-axis (cosine axis) and y-axis (sine axis).
• Draw a unit circle (radius = 1 unit) centered at the origin (0,0).

2. Identify Quadrantal Angles:

Quadrantal angles lie along the axes:

• 0° (or 360°) → Positive x-axis
• 90° → Positive y-axis
• 180° → Negative x-axis
• 270° → Negative y-axis

3. Plot the Points on the Unit Circle:

• For each quadrantal angle, the terminal side lies on the x-axis or y-axis.
• The coordinates of the point where the angle intersects the unit circle are:
• 0° (360°) → (1, 0)
• 90° → (0, 1)
• 180° → (-1, 0)
• 270° → (0, -1)

4. Determine Trigonometric Values:

Using the coordinates (x, y) on the unit circle:

• sin θ = y-coordinate
• cos θ = x-coordinate

5. Observations:

• sin θ is 0 at 0°, 180°, and 360° (where y = 0).
• cos θ is 0 at 90° and 270° (where x = 0).

6. Verification Using Graph:

• For 90°, the point is (0,1).
• sin 90° = 1 (y-coordinate).
• cos 90° = 0 (x-coordinate).
• For 180°, the point is (-1,0).
• sin 180° = 0 (y-coordinate).
• cos 180° = -1 (x-coordinate). And so on.

Conclusion:

By plotting quadrantal angles on a graph sheet and observing their intersection points with the unit circle, students can visually determine the values of sine, cosine, and tangent for these angles.

This activity reinforces the understanding of trigonometric functions and their behaviour at key angles.

Students Enjoyed learning through Hands on Experience👍

Output: