MAT1510 ASSIGNMENT 4 2023

MAT1510
ASSIGNMENT 4
2023

, QUESTION 1




Solution:



1.1).



a).


11π
(x, y) = (cos(t) , sin(t)) ∴t=
6
11π 11π
(x, y) = (cos ( ) , sin ( ))
6 6
√3 1
(x, y) = ( ,− )
2 2

, b).


4π
(x, y) = (cos(t) , sin(t)) ∴t=−
3
4π 4π
(x, y) = (cos (− ) , sin (− ))
3 3
1 √3
(x, y) = (− , )
2 2



c).


5π
(x, y) = (cos(t) , sin(t)) ∴t=
4
5π 5π
(x, y) = (cos ( ) , sin ( ))
4 4
√2 √2
(x, y) = (− ,− )
2 2



1.2).


4 3
( , ) = (cos(t) , sin(t))
5 5


4 3
cos(t) = and sin(t) =
5 5


a).



(x, y) = (cos(−t) , sin(−t)) ∴ cos(−t) = cos(t) and sin(−t) = − sin(t)
(x, y) = (cos(t) , − sin(t))
4 3
(x, y) = ( , − )
5 5