91Ó°ÊÓ

To understand coterminal angles, it's essential to first grasp the basics of angle measurement. Angles can be measured in degrees or radians, but in this discussion, we will focus on degrees. A full circle, or one complete revolution, measures 360 degrees. When an angle is drawn, it starts from the positive x-axis and rotates counterclockwise. The amount of rotation, measured in degrees, defines the angle. For instance, a 90° angle makes a quarter turn, whereas a 360° angle makes a full circle. Large angles, like 1055°, can be tricky, but remember they just indicate multiple full circles plus some extra rotation. That’s why we use the concept of coterminal angles to simplify.

To find coterminal angles, you need to subtract or add 360° multiple times until the result falls within the standard 0° to 360° range. Let's apply this method to the example given: the angle 1055°. Start by subtracting 360° repeatedly:

First step: 1055° - 360° = 695°
Second step: 695° - 360° = 335°

This process helps us find the 'simpler' angle (335°) that shares the same terminal side as 1055°. It's like peeling off the extra full circles until you're left with just one incomplete turn. This method ensures you find an equivalent angle that is easier to compare and work with.

Once you've identified the simplified (or coterminal) angle, compare it with the other given angle to determine if they are coterminal. In the example, we found that 1055° is coterminal with 335°. Now, compare this with the second angle: 155°. Since 335° does not equal 155°, these two angles are not coterminal. Remember that for two angles to be coterminal, their difference must be a multiple of 360°. In other words, \(|335° - 155°| \) must equal 360°k, where k is an integer. Since 335° - 155° = 180°, and 180° is not a multiple of 360°, these angles are not coterminal. Thus, understanding how to simplify and compare angles is crucial for working with coterminal angles.