SOLUTION: If the terminal Ray of alpha lies in third quadrant and that of Beta lies in first quadrant then the terminal ray of Alpha minus beta lies in......... Quadrant Sir plz explain w

Algebra ->  Angles -> SOLUTION: If the terminal Ray of alpha lies in third quadrant and that of Beta lies in first quadrant then the terminal ray of Alpha minus beta lies in......... Quadrant Sir plz explain w      Log On


   

Question 1081838: If the terminal Ray of alpha lies in third quadrant and that of Beta lies in first quadrant then the terminal ray of Alpha minus beta lies in......... Quadrant
Sir plz explain with details
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Alpha is quadrant 3 (Q3) so alpha is between 180 degrees and 270 degrees.

Beta is quadrant 1 (Q1) so beta is between 0 degrees and 90 degrees.

Let gamma = alpha-beta

The variable gamma is restricted with this inequality 90 < gamma < 270

The lower bound of 90 is from the fact that alpha - beta = 180-90 = 90 (where alpha = 180 and beta = 90)

The upper bound of 270 is from the fact that alpha - beta = 270-0 = 270 (where alpha = 270 and beta = 0)

So the angle gamma, aka alpha-beta, is located in quadrant 2 or in quadrant 3.