In the unit circle shown in the accompanying diagram, what are the coordinates of (x, y)?

It seems that your question references a specific diagram of a unit circle, but I unfortunately do not have access to images or diagrams. However, I can explain how to determine the coordinates (x, y) for points on the unit circle.

Understanding the Unit Circle

1. Definition of the Unit Circle: The unit circle is a circle with a radius of 1 centered at the origin (0,0) in the Cartesian coordinate plane. The equation of the unit circle is given by: $x^2 + y^2 = 1$

2. Coordinates on the Unit Circle: Points (x, y) on the unit circle represent the cosine and sine of an angle θ, where: $x = \cos(\theta) \quad \text{and} \quad y = \sin(\theta)$ Here, Θ is the central angle measured from the positive x-axis.

Determining Coordinates

1. Identify the Angle: If you know the angle θ corresponding to your desired point on the unit circle, you can directly find the coordinates.

2. Calculate Cosine and Sine: Substitute the angle into the cosine and sine functions to get the x and y coordinates:

   • $x = \cos(θ)$
   • $y = \sin(θ)$

Conclusion

If you have a specific angle in mind or further information about the location of the point in the circle, please provide it for a more precise answer regarding the coordinates (x, y). Generally, the coordinates can vary, but they will always satisfy the equation of the unit circle $(x^2 + y^2 = 1)$.