Understanding Angles in Standard Position and Coterminal Angles
TLDR; Understanding angles in standard position, quadrantal angles, and coterminal angles.
⭐ Angles in Standard Position
An angle is in standard position if its vertex is at the origin and the initial side is on the positive x-axis.
Angles in standard position are said to lie in the quadrant in which their terminal side lies.
General angles between 0 and 90 degrees lie in the first quadrant, between 90 and 180 in the second quadrant, between 180 and 270 in the third quadrant, and between 270 and 360 in the fourth quadrant.
🔀 General Angles
Angles between specific degree ranges are associated with particular quadrants.
Quadrantal angles, such as 90, 180, and 270 degrees, have their terminal side lying on one of the axes.
🔄 Coterminal Angles
Coterminal angles are angles in standard position that have a common terminal side.
Angles such as 30, 390, and -330 degrees are presented as examples of coterminal angles.
Coterminal angles can be positive or negative and are determined by the rotation from the initial side to the terminal side.
🌐 Coterminal Angles
Finding two angles that are coterminal with 135 degrees involves adding or subtracting 360 degrees to the given angle.
For example, 135 degrees and 495 degrees are coterminal angles.
The process of finding negative coterminal angles involves subtracting 360 degrees from the given angle.
🔍 Least Positive Angles
Determining the least positive coterminal angle to a given angle involves calculating the remainder when dividing by 360 degrees.
For instance, the least positive coterminal angle to 1070 degrees is found to be 350 degrees.
Another approach is to add or subtract multiples of 360 degrees to find the least positive coterminal angle.
🔄 Expressions
An expression for all angles coterminal to 90 degrees can be represented as 90 degrees plus or minus multiples of 360 degrees, where N is any integer.
This allows for the representation of an infinite number of coterminal angles to 90 degrees.