X = Cost Ost= 271 B X = cost A Osts 2 IT y = sint ( y = sin 2t Find cartesian equation for A and B and restricted domain for A and B using equation foundMethod - I since we have given 2 = Cos 2t Ost s 2 IT = sint The Domain of t variable is te[o, 217] DC = Cosit we meed to think about the minimum and maximum value of cost for E E[o,RIT] inorder to find Domain for ours Cartesian equation. let's start with the boundary values t=0 = cos ( 2 X0) 5 COS (0) = 1 = cos ( 2X217 ) = (oslyn ) = " we also know that cose has minimum value at 0= 17 as cost = 1 So in order to get the IT in cos(at), we put t= M2 E Co , 217] cos ( 2 x 17 ) 5 COS ( IT ) 5 - 1 since Coso E [ - 1 , 2 ), implies coszte [1," ) and we have found the value for which coset is -1 and 1 we cam say DC = cosit [- 1 , ]] = ) 2 = [-1, 2] or |- 1 5 x's 1 Similarly we fam do for Part B as well as y culso.Method - 2 Other way of thinking could be Since coso E [ - 1 , 1) and also (oszoe [ - 1, 1) as well as simo E [ - 1, 1] also sinzoe [-1, 1] fors Of [ 0 , 217] [ We knew this thing from basic Toryomomatry ] ard T our case also t E [o,zn], which simply implies that RE[ - 1 1 1 ) X & COs 26 7 & y 6 [ - 1 12 g= sint = cost # DE [ 1 ,1 ] B y = sinzt & J e [ - 1 1] ] Here Just think instead of in your basic trigonomatory understanding, you will set it easily