#### Math - 2018-19

# T.2 - Unit Circle

T.2The student willdevelopandapplythe properties of the unit circle in degrees and radians.

*Adopted: 2016*

### BIG IDEAS

### UNDERSTANDING THE STANDARD

· 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.2_{1}** Define**
the six circular trigonometric functions of an angle in standard position.

·
T.2_{2}** 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.2_{3}** 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*