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

r = b - a

s = a + b

u = 2 b

t = - a

 Mar 28, 2022

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

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

Thank you ElectricPavlov, it makes sense now.

 Mar 28, 2022

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