Question

If on the unit circle c, the distance from p(1, 0) to the point t ( , ) is x, determine the coordinates of the point at the indicated distance from p: x.

1) (-4/5, 3/5)
2) (4/5, -3/5)
3) (4/5, 3/5)
4) (-4/5, -3/5)

Answer 1

To determine the coordinates of the point at the indicated distance from p, we can use the concept of polar coordinates on the unit circle. The correct coordinates for the indicated distance are (4/5, -3/5).

Step-by-step explanation:

To determine the coordinates of the point at the indicated distance from p, which is x, we can use the concept of polar coordinates. The distance x is given as the distance from the point p(1, 0) to the point t. On the unit circle, the point t can be represented by the coordinates (cosθ, sinθ), where θ is the angle. From the given options, we need to find the point that lies at x distance from p on the unit circle.

Since p(1, 0) lies on the x-axis, the y-coordinate of the point t will be equal to sinθ. We can use the Pythagorean identity x^2 + y^2 = 1 to find the x-coordinate:

x^2 + sin^2θ = 1

x^2 = 1 - sin^2θ

x = sqrt(1 - sin^2θ)

Therefore, the coordinates of the point at the indicated distance x from p on the unit circle would be (sqrt(1 - sin^2θ), sinθ).

By comparing the options given, we can determine that the correct answer is (2) (4/5, -3/5), as it satisfies the conditions for the x-coordinate and y-coordinate.