# T.2 - Unit Circle

T.2  The student will develop and apply the properties of the unit circle in degrees and radians.

### UNDERSTANDING THE STANDARD

2016 VDOE Curriculum Framework - T.2 Understanding

·  Triangular trigonometric function definitions are related to circular trigonometric function definitions.

·  Knowledge of the unit circle is a useful tool for determining all six trigonometric values for special angles (30°, 45°, 60°, and 90°).

·  The relationships between the angle measures and side lengths of special right triangles (30°-60°-90° and 45°-45°-90°) are widely used in mathematics.

·  Special right triangles may be used to develop the unit circle.

·  Unit circle properties will allow special angle and related angle trigonometric values to be found without the aid of a graphing utility.

·  Degrees and radians are units of angle measure.

·  A radian is the measure of the central angle that is determined by an arc whose length is the same as the radius of the circle.

·  There is a connection between sides and angles of special right triangles, the unit circle, and the coordinate plane.

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

·  T.21  Define the six circular trigonometric functions of an angle in standard position.

·  T.22  Apply the properties of the unit circle to determine trigonometric function values of special angles and their related angles in both degrees and radians without using a graphing utility.

·  T.23  Apply the properties of the unit circle to convert between special angles expressed in radians and degrees, without using a graphing utility.

### KEY VOCABULARY

Updated: May 29, 2018