Question

Match the x-coordinates with their corresponding pairs of y-coordinates on the unit circle.

1) (0, 1)
2) (1, 0)
3) (-1, 0)
4) (0, -1)

Answer 1

The x-coordinates and their corresponding pairs of y-coordinates on the unit circle are (0, 1), (1, 0), (-1, 0), and (0, -1). The x-coordinate represents the cosine value and the y-coordinate represents the sine value.

Step-by-step explanation:

The x-coordinates and their corresponding pairs of y-coordinates on the unit circle are:

1. (0, 1)
2. (1, 0)
3. (-1, 0)
4. (0, -1)

The x-coordinate represents the cosine value and the y-coordinate represents the sine value. For example, when the x-coordinate is 0 and the y-coordinate is 1, it means that the cosine is 0 and the sine is 1. These values are important in trigonometry and can be used to calculate various angles and distances.

Answer 2

The x-coordinates on the unit circle correspond to the cosine of the angle, and the y-coordinates to the sine. The student's question is about matching these points, which represent key angles: 90°, 0°, 180°, and 270°, leading to matches of the given points with (0, 1), (1, 0), (-1, 0), and (0, -1).

Step-by-step explanation:

The student is asking to match the x-coordinates with their corresponding pairs of y-coordinates on the unit circle. On the unit circle, any point is represented as (x, y), where the value of x is the cosine of the angle from the positive x-axis, and the value of y is the sine of the angle. Here are the matches:

• (0, 1) corresponds to the angle of 90° or π/2 radians. The sine is 1 and cosine is 0.
• (1, 0) corresponds to the angle of 0° or 0 radians. The sine is 0 and cosine is 1.
• (-1, 0) corresponds to the angle of 180° or π radians. The sine is 0 and cosine is -1.
• (0, -1) corresponds to the angle of 270° or 3π/2 radians. The sine is -1 and cosine is 0.

The answers are therefore: (1) matches with 3 (-1, 0), (2) matches with 4 (0, -1), (3) matches with 2 (1, 0), and (4) matches with 1 (0, 1).