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Let  \(\alpha \) and \(\beta\) be angles such that  is the terminal point for \(a \) and \(Q\)  is the terminal point for \(\beta \) . Let \(R, S, T, U\)  be other terminal points below:
 

 

Then \(R, S, T, U\) are the terminal points for the angles \(\alpha+\beta, \beta-\alpha, 2\beta, -\alpha\)  in some order.

 

\(R, S, T, U\)

 

Order the terminal pointsto match the angles above.

 Mar 28, 2022
 #1
avatar+36434 
+1

r = b - a

s = a + b

u = 2 b

t = - a

 Mar 28, 2022
 #2
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+1

Hello ElectricPavlov, 

 

Thank you very much for the response, I greatly appreciate your help. Can you please explain your thought process for solving this question? It would really help me in future problems such as this. 

Guest Mar 28, 2022
 #3
avatar+36434 
+2

For clarity, I re-labelled the points   alpha and beta in the diagram below

 

 

   Now if you look at point R    you can see that it is just point  b   minus the amount of point  a    ......   right?

      similarly    point   b    PLUS the maount of point  a     would land you at  S

        b   is approximately 145 degrees      2 * 145 = 290 degrees ....which would be point  U

              look at point  a     go the same amount in the clockwise direction from the x-axis to get to   -a  ...... this would be point  T

 

 

 

 

ElectricPavlov  Mar 28, 2022
 #4
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+1

Thank you ElectricPavlov, it makes sense now.

 Mar 28, 2022

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