Quadrantal & Refetence Angles

[nycmathguy]

Section 4.4

In your own words, define the following two angles:

1. Quadrantal

2. Reference

 

[MathLover1]

Quadrantal Angle
Angles in the standard position where the terminal side lies on the x or y axis. For example: 90°, 180° etc.
A quadrantal angle is one that is in the standard position and has a measure that is a multiple of 90° (or π/2 radians). A quadrantal angle will have its terminal lying along an x or y axis.

Reference angle
The smallest angle that the terminal side of a given angle makes with the x-axis. It is always positive and always less than or equal to 90°, even for very large angles.
Depending on the quadrant, find the reference angle:
Quadrant......... Reference angle for θ
1..................Same as θ
2..................180 - θ
3..................θ - 180
4..................360 - θ

Coterminal angles

wo angles are coterminal if they are drawn in the standard position and both have their terminal sides in the same location.
Either or both angles can be negative.
If the angle is positive, keep subtracting 360 from it until the result is between 0 and 360. (In radians, 360° = 2π radians)
If the angle is negative, keep adding 360 until the result is between 0 and 360.
If the result is the same for both angles, they are coterminal.

 

[nycmathguy]

Quadrantal Angle
Angles in the standard position where the terminal side lies on the x or y axis. For example: 90°, 180° etc.
A quadrantal angle is one that is in the standard position and has a measure that is a multiple of 90° (or π/2 radians). A quadrantal angle will have its terminal lying along an x or y axis.

Reference angle
The smallest angle that the terminal side of a given angle makes with the x-axis. It is always positive and always less than or equal to 90°, even for very large angles.
Depending on the quadrant, find the reference angle:
Quadrant......... Reference angle for θ
1..................Same as θ
2..................180 - θ
3..................θ - 180
4..................360 - θ

Coterminal angles

wo angles are coterminal if they are drawn in the standard position and both have their terminal sides in the same location.
Either or both angles can be negative.
If the angle is positive, keep subtracting 360 from it until the result is between 0 and 360. (In radians, 360° = 2π radians)
If the angle is negative, keep adding 360 until the result is between 0 and 360.
If the result is the same for both angles, they are coterminal.

Thank you for the reference angle table. This is very useful information.