Main Activity-2: Cofunction Angle 90°
Goal:
Demonstrate why trigonometric function names change when using the vertical Y-axis (90°) as a reference.
Description:
When we measure an angle from the vertical Y-axis, the triangle "tips over." The side that was "Opposite" to the angle becomes "Adjacent" to the complementary angle. This geometric swap is why Sine (Opposite) becomes Cosine (Adjacent).
Instructions:
1. Set the slider to an angle between 0° and 180° (e.g., 50°).
The gray angle shows how far your angle is from the 90° line.
Notice how the applet rewrites the angle as (90° - + x).
2. Look at the right triangle formed by this gray angle near the 90° reference axis.
- Examine the sides of this small triangle.
- Which side is opposite to the gray angle?
- Which side is adjacent to the gray angle?
- How do these compare to the opposite and adjacent sides of the original large-angle triangle?
Write your answers in the given space below each question.
Indicate whether it is True (T) or False (F) for each statement below.
1) For every complementary angles a and b, such that a + b = 90⁰ sin(a) = cos(b)
2) For 0° < x < 90°, cot(90° + x) = cot(x)
3) For 0° < α < 90°, cos(90° + α) = –sin(α)
Using cofunction identities, solve for x in each equation below.
4) cot(48°) = tan(x) x = ?
5) cot(110°) = – tan(x) x = ?
6) cos(62°) = sin(x) x = ?
(Be careful!) 7) sin(50°) = – sin(x) x = ?