The point (-1, 0) is a specific coordinate on the unit circle, which is a circle with a radius of 1 unit centered at the origin (0, 0) on the Cartesian coordinate plane. The coordinates (-1, 0) represent a point on the unit circle that corresponds to a specific angle and trigonometric function values.
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The point (-1, 0) on the unit circle corresponds to an angle of 180 degrees or $\pi$ radians.
At the point (-1, 0), the sine function has a value of 0, the cosine function has a value of -1, and the tangent function is undefined.
The point (-1, 0) represents the end of the negative x-axis on the unit circle, where the angle is 180 degrees or $\pi$ radians.
The coordinates (-1, 0) are used to study the behavior and properties of trigonometric functions, such as their periodicity and symmetry.
Understanding the significance of the point (-1, 0) on the unit circle is crucial for solving problems involving trigonometric functions and their applications.
Review Questions
Explain the significance of the point (-1, 0) on the unit circle and its relationship to trigonometric functions.
The point (-1, 0) on the unit circle represents an angle of 180 degrees or $\pi$ radians. At this point, the sine function has a value of 0, the cosine function has a value of -1, and the tangent function is undefined. This point is located at the end of the negative x-axis on the unit circle and is an important reference point for understanding the behavior and properties of trigonometric functions, such as their periodicity and symmetry.
Describe how the coordinates (-1, 0) are used to analyze the values of trigonometric functions on the unit circle.
The coordinates (-1, 0) on the unit circle are used to study the values of the trigonometric functions sine, cosine, and tangent at an angle of 180 degrees or $\pi$ radians. At this point, the sine function has a value of 0, the cosine function has a value of -1, and the tangent function is undefined. These values are crucial for understanding the periodic nature of trigonometric functions and their applications in various fields, such as engineering, physics, and mathematics.
Analyze how the point (-1, 0) on the unit circle relates to the symmetry and periodicity of trigonometric functions.
The point (-1, 0) on the unit circle represents a key point of symmetry and periodicity for trigonometric functions. The fact that the sine function has a value of 0 and the cosine function has a value of -1 at this point demonstrates the even and odd symmetry of these functions, respectively. Additionally, the point (-1, 0) is located at an angle of 180 degrees or $\pi$ radians, which is a critical reference point for understanding the periodic nature of trigonometric functions and their applications in various fields, such as wave behavior, periodic phenomena, and the analysis of complex waveforms.
The measure of rotation between two intersecting lines or planes in a circular or spherical coordinate system, typically measured in degrees or radians.
The functions sine, cosine, and tangent, which relate the angles of a triangle to the lengths of its sides, and are used to study periodic phenomena and wave-like behavior.