Main Activity-3: Cofunction Angle 270°
Goal:
Demonstrate why trigonometric function names change and signs reverse when using the vertical Y-axis (270°) as a reference.
Description:
Just like at 90°, the 270° line is a vertical reference. This means the triangle "tips over" again, causing the "Opposite" and "Adjacent" sides to swap roles. Therefore, Sine becomes Cosine. However, in the 3rd and 4th quadrants, we must also carefully check the coordinate signs.
Instructions:
1. Set the slider 
to an angle between 180° and 360° (eg: 240°).
2. Think of the negative Y-axis (270°) as your new reference line.The gray angle shows how far your angle is from 270°.So the angle is rewritten as (270+-x) (e.g: 270 - 30⁰)
3. Focus on the right triangle formed by this gray angle near the 270° reference axis.
to an angle between 180° and 360° (eg: 240°).
2. Think of the negative Y-axis (270°) as your new reference line.The gray angle shows how far your angle is from 270°.So the angle is rewritten as (270+-x) (e.g: 270 - 30⁰)
3. Focus on the right triangle formed by this gray angle near the 270° reference axis.
- Examine the sides of this small triangle?
- What is the length of the vertical side, sin(x)?
- What is the length of the horizontal side, cos(x)?
- How do these compare to the sides of the original large-angle triangle?
Observe:
What happens with the 'Opposite' and 'Adjacent' sides lenghts a and b, when we look at the triangle of the complementary angle?
Wrapping up:
Imagine you are writing a cheat sheet for a friend. How would you explain the rule for ANY angle involving 90° or 270° versus 180° or 360°?