Find the reference angle for each angle.
205°

Key Concepts

Reference Angle

The reference angle is the acute angle formed by the terminal side of a given angle and the x-axis. It is always measured as a positive angle and is used to simplify the calculation of trigonometric functions. For angles greater than 180°, the reference angle is found by subtracting the angle from 360° or 180°, depending on the quadrant in which the angle lies.

Quadrants of the Unit Circle

The unit circle is divided into four quadrants, each representing a range of angles. The first quadrant (0° to 90°) contains angles where both sine and cosine are positive. The second quadrant (90° to 180°) has positive sine and negative cosine, the third quadrant (180° to 270°) has both negative sine and cosine, and the fourth quadrant (270° to 360°) has positive cosine and negative sine. Understanding these quadrants is essential for determining the reference angle.

Angle Measurement

Angles can be measured in degrees or radians, with degrees being the more common unit in basic trigonometry. A full circle is 360°, and angles can be classified as acute (less than 90°), right (90°), obtuse (between 90° and 180°), and reflex (greater than 180°). Knowing how to convert between degrees and radians is important for solving trigonometric problems, especially when dealing with reference angles.