In Exercises 44–48, find the reference angle for each angle. -410°

Verified step by step guidance

1. <Convert the given angle to a positive angle by adding 360° until the angle is positive.>
2. <Once you have a positive angle, determine if it is greater than 360°. If so, subtract 360° to find the equivalent angle within one full rotation.>
3. <Identify the quadrant in which the angle lies.>
4. <Use the quadrant information to find the reference angle. For angles in the third quadrant, subtract 180° from the angle.>
5. <Express the reference angle as a positive acute angle, which is always between 0° and 90°.>

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 less than 0°, the reference angle can be found by first determining the equivalent angle within the standard range of 0° to 360°.

Angle Coterminality

Coterminal angles are angles that share the same terminal side when drawn in standard position. To find a coterminal angle, you can add or subtract multiples of 360° from the original angle. For example, to find a coterminal angle for -410°, you would add 360° until the angle falls within the range of 0° to 360°.

Quadrants of the Coordinate Plane

The coordinate plane is divided into four quadrants, each representing a different 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 in determining the reference angle and its corresponding sine, cosine, and tangent values.