Find all angles è between 0° and 180° satisfying the given equation.

cos è = 1/9

cosθ = 1/9

θ = 83.6°
That is your reference angle.

Since cosine is positive in QI and QIV, your two angles are

83.6° and (360-83.6)°

To find all angles è between 0° and 180° satisfying the equation cos è = 1/9, we can use the inverse cosine function (also known as arccosine or cos⁻¹).

1. First, calculate the inverse cosine of 1/9.
arccos(1/9) ≈ 82.819°

2. Since the cosine function has a periodicity of 360°, we know that there are infinitely many angles that satisfy the equation. We just need to find the other angles within the specified range.

3. To find the other angle, subtract the original angle from 180°.
180° - 82.819° ≈ 97.181°

So, we have two angles:
- Angle è1 ≈ 82.819°
- Angle è2 ≈ 97.181°

These are the two angles between 0° and 180° that satisfy the equation cos è = 1/9.