In Exercises 35–60, find the reference angle for each angle.355°

Verified step by step guidance

1. Identify the given angle: 355°.
2. Determine if the angle is greater than 360° or less than 0°. Since 355° is between 0° and 360°, it is already in standard position.
3. Find the reference angle by subtracting the given angle from 360°: Reference angle = 360° - 355°.
4. The reference angle is the acute angle formed with the x-axis, which is always positive and less than 90°.
5. Conclude that the reference angle for 355° is the result from the subtraction in step 3.

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 360° or negative angles, the reference angle can be found by first reducing the angle to its equivalent within the standard range of 0° to 360°.

Angle Reduction

Angle reduction involves converting an angle that exceeds 360° or is negative into an equivalent angle within the standard range of 0° to 360°. This is done by subtracting or adding 360° as necessary. For example, to find the equivalent angle of 355°, you can simply use it as is since it is already within the desired range.

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 helps determine the reference angle, as it influences the calculation of the acute angle with respect to the x-axis.