SOLUTION: Eliminate θ from these equation (i) x = sinθ + tanθ, y = sinθ - tanθ (ii) x = atanθ, y = bcosθ (iii) x = 1 + tanθ, y = cosθ

Algebra ->  Test -> SOLUTION: Eliminate θ from these equation (i) x = sinθ + tanθ, y = sinθ - tanθ (ii) x = atanθ, y = bcosθ (iii) x = 1 + tanθ, y = cosθ      Log On


   

Question 1152029: Eliminate θ from these equation
(i) x = sinθ + tanθ, y = sinθ - tanθ
(ii) x = atanθ, y = bcosθ
(iii) x = 1 + tanθ, y = cosθ
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.

            In my post,  I will solve part  (ii)  only. 


Start from the standard trigonometry identity

    1%2F%28tan%5E2%28theta%29%2B1%29 = cos%5E2%28theta%29.            (1)



From the given part of  (ii),  

    tan%28theta%29 = x%2Fa  and  cos%28theta%29 = y%2Fb.     (2)



Now replace in (1)  tan%28theta%29  by  x%2Fa  and  replace  cos%28theta%29  by  y%2Fb,  based on (2).  You will get


    1%2F%28%28x%2Fa%29%5E2%2B1%29 = %28y%2Fb%29%5E2.                 (3)


Thus we just eliminated  theta  and obtained  the relationship  (the equation) for x and y.


The goal is reached:  the problem is just solved in this way.


You may simplify the equality  (4)  further as you want.