In Exercises 44–48, find the reference angle for each angle.265°

Verified step by step guidance

1. Identify the given angle: 265°.
2. Determine which quadrant the angle is in by noting that angles between 180° and 270° are in the third quadrant.
3. Recall that the reference angle is the acute angle formed by the terminal side of the given angle and the x-axis.
4. For angles in the third quadrant, the reference angle is found by subtracting 180° from the given angle.
5. Calculate the reference angle: 265° - 180°.

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 typically between 0° and 90°. For angles greater than 180°, the reference angle helps simplify trigonometric calculations by relating the angle to its corresponding acute angle.

Quadrants of the Unit Circle

The unit circle is divided into four quadrants, each representing a range of angles. The first quadrant contains angles from 0° to 90°, the second from 90° to 180°, the third from 180° to 270°, and the fourth from 270° to 360°. Understanding which quadrant an angle lies in is essential for determining its reference angle and the signs of its trigonometric functions.

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 exceed this range, necessitating the need to find equivalent angles within the standard range. For example, an angle of 265° can be converted to a reference angle by subtracting it from 360° or determining its position relative to the nearest x-axis.