Speculation has been rife following the departure of Michael Laudrup, but the win over Cardiff and well-earned midweek point at Stoke settled suggestions the club was in disarray.
One of the accusations levelled at Laudrup was the development of a dressing room split between Spanish and British players, something Garry Monk was quick to play down on his appointment last week - and Rangel has equally admonished the claims.
"You can trust me, I've been here long enough and seen many Spanish players in the squad - including myself - and the unity has always been one of the key things at Swansea City," he told Wales Online. "We've seen that over the years and it's still the case.
"Things like the language barrier will always be an issue but we are a team and you could see at Stoke there are no enemies only team-mates; you can see a togetherness.
"We heard similar things last year, that the players were not getting on with the manager, blah, blah, blah, but we proved everyone wrong and we're showing again we are all together."
He added: "It is the same about players who the last manager brought in. It is natural that if a manager signs you and then is sacked you may worry that you may go out of the side but I think Garry has made sure that doesn't happen.
"He has involved every single player and we are all working together and fighting together for one thing: survival."
Rangel will be helping Swansea fight for a place in the quarter-finals of the FA Cup rather than survival on Sunday, but insists the signs of progression under Monk are already there to see.
"We showed our mentality in coming from behind against Stoke," Rangel said. "He has raised the tempo on and off the ball in terms of on the pitch, but he has also made sure we have showed a lot of pride and working for each other.
"It is early but you can see similarities with Roberto and with Brendan on the training ground which is great because they are both showing they are great managers, that shows you Garry has learned from the best in this style of football in this country.
"He is still young and will be learning but you can see if he keeps going the same way he will become a great head coach.
"We are not safe but it is a sign that we are moving in the right direction and things are optimistic again. The next few games we must show the same character and play the same football and we will be okay."