(0, 1)

Definition

(0, 1) is a point on the unit circle, which is a circle with a radius of 1 unit centered at the origin (0, 0) in the coordinate plane. The point (0, 1) represents the angle of 90 degrees or $\pi/2$ radians on the unit circle.

5 Must Know Facts For Your Next Test

1. The point (0, 1) on the unit circle represents the angle of 90 degrees or $\pi/2$ radians.
2. The x-coordinate of the point (0, 1) is 0, and the y-coordinate is 1.
3. The point (0, 1) is the positive y-intercept of the unit circle, indicating that the sine function is equal to 1 at this angle.
4. The cosine function is equal to 0 at the point (0, 1), as the x-coordinate is 0.
5. The tangent function is undefined at the point (0, 1), as the cosine value is 0, resulting in a division by zero.

Review Questions

• Explain the significance of the point (0, 1) on the unit circle and how it relates to trigonometric functions.
  • The point (0, 1) on the unit circle represents the angle of 90 degrees or $\pi/2$ radians. This point is significant because it is the positive y-intercept of the unit circle, indicating that the sine function is equal to 1 at this angle. Additionally, the cosine function is equal to 0 at this point, and the tangent function is undefined due to the cosine value being 0, resulting in a division by zero. Understanding the coordinates and trigonometric function values at the point (0, 1) is crucial for solving problems involving the unit circle and trigonometric functions.
• Describe how the point (0, 1) on the unit circle is used to define the sine, cosine, and tangent functions.
  • The point (0, 1) on the unit circle is used to define the trigonometric functions as follows: The y-coordinate of the point (0, 1) is 1, which corresponds to the value of the sine function at an angle of 90 degrees or $\pi/2$ radians. The x-coordinate of the point (0, 1) is 0, which corresponds to the value of the cosine function at this angle. The tangent function is undefined at this point because the cosine value is 0, resulting in a division by zero. Understanding the relationship between the coordinates of the point (0, 1) and the trigonometric function values is essential for applying these functions in various mathematical and real-world contexts.
• Analyze the significance of the point (0, 1) on the unit circle and how it relates to the behavior of the sine, cosine, and tangent functions.
  • The point (0, 1) on the unit circle is a critical point that defines the behavior of the trigonometric functions. At this point, the sine function reaches its maximum value of 1, indicating that the angle of 90 degrees or $\pi/2$ radians corresponds to the point where the sine function is at its peak. Conversely, the cosine function is equal to 0 at this point, meaning that the angle of 90 degrees or $\pi/2$ radians is where the cosine function crosses the x-axis. Additionally, the tangent function is undefined at the point (0, 1) because the cosine value is 0, resulting in a division by zero. Understanding the significance of the point (0, 1) and its relationship to the trigonometric functions is essential for analyzing the properties and behaviors of these functions in various mathematical and real-world applications.

Related terms

Unit Circle: The unit circle is a circle with a radius of 1 unit centered at the origin (0, 0) in the coordinate plane. It is used to define trigonometric functions and their relationships.

Angle Measure: Angle measure refers to the amount of rotation around a circle, typically measured in degrees or radians. The point (0, 1) on the unit circle corresponds to an angle of 90 degrees or $\pi/2$ radians.

Trigonometric Functions: Trigonometric functions, such as sine, cosine, and tangent, are defined using the coordinates of points on the unit circle. The point (0, 1) is the y-coordinate of the sine function at an angle of 90 degrees or $\pi/2$ radians.