I need help creating a query

Hello,

I need a little help creating a query, I have two tables, worker and position, for simplicity sake worker only has its ID and its name, position has the ID of the worker, the name of his position, a date, and his salary/

worker:   worker_id, name
position: position_id, worker_id, position, startdate, salary

If I perfom a query joining both tables, I can obtain all the workers and the positions the've had.

SELECT name, startdate, position,  salary FROM worker JOIN position USING(worker_id);
worker1 | 2001-01-01 | boss             | 999999
worker2 | 2001-01-01 | cleaning        | 100
worker2 | 2006-04-01 | programmer   | 20000
worker2 | 2006-07-04 | management | 25000

so far so good, now I need to obtain all the workers only with the position they had on a given date.
if I wanted to know the positions on '2006-05-01' it would return
worker1 | 2001-01-01 | boss             | 999999
worker2 | 2006-04-01 | programmer   | 20000

Maybe I only need some insight here, maybe it should be done with 2 queries, maybe it should be done with functions, I don't know.

Thanks