Final answer:
To express the given points on the unit circle, for Quad I, the coordinates are (0.9879, 0.16), for Quad II, the coordinates are (-1/2, √3/2), for Quad III, the coordinates are (-√3/2, -1/2), and for Quad IV, the coordinates are (0.9408, -0.34).
Step-by-step explanation:
To show three different ways of expressing points on the unit circle, we need to find the corresponding coordinates for each quadrant. For Quad I, where y = 0.16, we have x = √(1 - y²) = √(1 - 0.16²) = √0.97424 ≈ 0.9879. Therefore, the point in Quad I is (0.9879, 0.16).
For Quad II, where y = √3/2, we have x = -√(1 - y²) = -√(1 - (√3/2)²) = -√(1 - 3/4) = -√(1/4) = -1/2. Therefore, the point in Quad II is (-1/2, √3/2).
Similarly, for Quad III, where x = -√3/2, we have y = -√(1 - x²) = -√(1 - (-√3/2)²) = -√(1 - 3/4) = -√(1/4) = -1/2. Therefore, the point in Quad III is (-√3/2, -1/2).
In Quad IV, where y = -0.34, we have x = √(1 - y²) = √(1 - (-0.34)²) = √(1 - 0.1156) = √0.8844 ≈ 0.9408. Therefore, the point in Quad IV is (0.9408, -0.34).