Trigometric derivatives application

6.5 sin t An object moves along a line so that in t seconds its position is s(t) = 3 + cos 2t where s is 5.) the displacement in metres. Find the objects EXACT velocity at t = . (4 v marks) Hint: Remember there is a derivative rule that starts with a Q v (t ) = s'( t ) 2. s'(t ) = (cost) (3cos 2t) -(-sin 2t . 2 ) (sint) (3+ cos 2t) ? v ( +) = Bcos 2t ) (cost) + (2sin2()(sint) Sub in (3 + Cos 2 ( )2 right qhawa V.It) = 3 cost + cos 204 2,sin /tvint (3 + cos 2+)2 at f = ] v ( 1) ) = 3 cos ( P)+ cos 2 ( 2 ) 2 + 2vin2( # Join( 7: ) 3+ Cos 2/1) 2