Identify Quadrant of Angle (radians)

[Quincy]

Homework Statement

Determine the quadrant in which the terminal side of the angle lies. (The angle is given in radians.)

a) -1 b) -2

The Attempt at a Solution

a) -1 * (180/3.14) = -57.3 degrees -- Quadrant IV

b) -2 * (180/3.14) = -114.6 degrees -- Quadrant III

- Is there a way to find out which quadrant they're in without having to to convert them into degrees?

 

[HallsofIvy]

Well, how does knowing them in degrees help you? I assume it is because you know that 0, 90, 180, and 270 degrees, as well as -90, -180, and -270 are the "separators". You should know the same thing for radians. The corresponding values are 0, $\pi/2$= 0.785, $\pi/2$= 1.57, $3\pi/2$= 4.71, and the corresponding negative values.

 

[Architeuthis Dux]

Yes, there is a way to identify the quadrant of an angle given in radians without converting it into degrees. The quadrant of an angle in radians can be determined by looking at the sign of the angle. In the standard coordinate system, angles in Quadrant I have positive values, angles in Quadrant II have negative values, angles in Quadrant III have negative values, and angles in Quadrant IV have positive values. Therefore, for the given angles a) -1 and b) -2, we can determine that they are in Quadrants IV and III, respectively, without converting them into degrees. This is because both -1 and -2 are negative values, indicating that they lie in Quadrants IV and III, respectively.