495
Find three coterminal angles:
____________
____________
____________
Standard position angle:
Reference angle:
To find three coterminal angles, we can add or subtract multiples of 360 degrees (or 2π radians) to the given angle.
Given angle: 495 degrees
1. Adding 360 degrees:
495 + 360 = 855 degrees
2. Subtracting 360 degrees:
495 - 360 = 135 degrees
3. Adding another 360 degrees:
495 + 360 + 360 = 1215 degrees
Thus, three coterminal angles for 495 degrees are:
1. 495 degrees
2. 855 degrees
3. 135 degrees
For the standard position angle, we consider the angle in its initial position. In this case, the given angle of 495 degrees lies in the fourth quadrant when starting from the positive x-axis and rotating counterclockwise.
For the reference angle, we find the acute angle formed between the terminal side of the angle and the x-axis. To find it, we need to subtract multiples of 360 degrees from the given angle until it lies between 0 and 360 degrees.
495 - 360 = 135 degrees
Therefore, for the given angle of 495 degrees:
Standard position angle: Fourth quadrant
Reference angle: 135 degrees