Use the unit circle shown to find the value of the trigonometric function.
cos 𝜋/6

Verified step by step guidance

1. Identify the angle \( \frac{\pi}{6} \) on the unit circle. This angle corresponds to 30 degrees.
2. Recall that the unit circle is a circle with a radius of 1 centered at the origin of the coordinate plane.
3. On the unit circle, the coordinates of a point corresponding to an angle \( \theta \) are \((\cos \theta, \sin \theta)\).
4. For \( \theta = \frac{\pi}{6} \), find the x-coordinate of the point on the unit circle, which represents \( \cos \frac{\pi}{6} \).
5. Use the known values from the unit circle: \( \cos \frac{\pi}{6} = \frac{\sqrt{3}}{2} \).

Key Concepts

Unit Circle

The unit circle is a circle with a radius of one centered at the origin of a coordinate plane. It is a fundamental tool in trigonometry, as it allows for the definition of trigonometric functions based on the coordinates of points on the circle. The x-coordinate of a point on the unit circle corresponds to the cosine of the angle, while the y-coordinate corresponds to the sine.

Cosine Function

The cosine function, denoted as cos(θ), represents the x-coordinate of a point on the unit circle corresponding to an angle θ measured from the positive x-axis. For angles measured in radians, such as π/6, the cosine function provides a specific value that can be derived from the coordinates of the corresponding point on the unit circle.

Reference Angles

Reference angles are the acute angles formed by the terminal side of an angle and the x-axis. They are crucial for determining the values of trigonometric functions in different quadrants. For example, the angle π/6 has a reference angle of π/6 itself, which helps in finding its cosine value directly from the unit circle.