cos θ = (2√(2)) / (3)

sin θ = - (1/3)

then what would the triangle look like, the placement of the sides on quadrant 1,2,3, or 4?

To determine the placement of the sides of the triangle, we need to analyze the given values of cosine (cos θ) and sine (sin θ).

Given that cos θ = (2√2) / 3 and sin θ = -1/3, we can use the following information:

1. In quadrant I (top right), both cosine and sine are positive. However, the given value of sin θ = -1/3 is negative, so the position of θ cannot be in quadrant I.

2. In quadrant II (top left), cosine is negative, and sine is positive. The given value of cos θ = (2√2) / 3 is positive, indicating that it could possibly be in quadrant II.

3. In quadrant III (bottom left), both cosine and sine are negative. Again, the given value of cos θ = (2√2) / 3 is positive, indicating that it cannot be in quadrant III.

4. In quadrant IV (bottom right), cosine is positive, and sine is negative. The given value of sin θ = -1/3 is negative, suggesting that it might be in quadrant IV.

Based on this analysis, we can deduce that the triangle is located in either quadrant II or IV. The values of cos θ and sin θ alone do not allow us to determine the exact placement; additional information is required.