If Joe Gibbs had been able to master trigonometry the way he has mastered pass patterns, he probably would be directing a Fortune 500 corporation instead of figuring out how to beat Dallas next Sunday.

Like any other red-blooded American, Gibbs wanted to make lots of money when he grew up. He even had a plan for achieving this life of leisure.

"You had to major in math and science in college, those were the subjects you took if you wanted to be a scientist or an engineer, and that's where the money was at that time," Gibbs said.

But Gibbs blew the mathematics portion of his college entrance examination and wound up in a remedial math class at San Diego State.

"I went to the counselor and told her I had to get out, I couldn't stand it in that class any more," he said. "She told me I could leave if I changed my major."

That's all the prodding he needed. Out went math and science. In came physical education. Out went engineering. In came coaching -- football coaching.

"I always loved sports anyway, played them all, all the time," he said. "I was a sophomore, I guess, and a member of the football team when I decided that my life would be devoted to being a football coach."

Twenty years later, Gibbs has reached his goal at the relatively youthful age of 40. As the first-year head coach of the Redskins, he is continuing on what his friends have told him is a path guided by destiny.

"They think that everything has always worked out great for me, that I've had the good breaks all along the way," he said. "I don't think that is true.

"But I do think this. I'm convinced this is where I'm supposed to be and what I'm supposed to be doing at this time."

What better team for him than the Redskins, where the owner yearns for exciting teams and the fans for something other than a Woody Hayes offense?

And what better place for him than Washington, where a handsome, outgoing, articulate, intelligent, energetic coach who WINS can name his endorsements, television shows, personal appearances and other fringe benefits that turn a $110,000 annual salary into a corporate president's income?

Gibbs is bringing the offense of the future to a team that still labors in the shadow of the '70s, the George Allen '70s. He is a relative unknown hired to fill one of the most visible roles in a high-profile town eager to renew its love affair with the Redskins. And while Washington begins its courtship with this newest would-be hero, he will be trying to shorten the engagement with a crash course in the art of being a head coach.

Gibbs still may be relatively young but he admits there were times before the Redskin job became open that he felt he was already growing old.

"People would say I was so young, but I knew I had been in the business a long, long time," he said. "I'd look at 14 or 15 years go by and I'd say, 'For cripes sake, am I ever going to get a head coaching job?' I was supposed to be patient but from my point of view, after a couple of college chances came up and I didn't get them, you begin to wonder if you'd ever get a chance.

"All the moves I made in my career, I tried to make each an advancement, each a step toward a specific goal. I wanted to be a college head coach, but when that didn't seem the thing to do, I aimed for a similiar spot in the pros.

"But there was always pressure to be in a winning program, to have winning years. If you aren't surrounded by success, you can be in trouble. Your personal hopes can go down the tubes. So you want the team to win, but you also want them to win for selfish reasons."

Now Gibbs has the most selfish of all reasons to win: job security. He may not need a magical season this year, but owner Jack Kent Cooke is not a believer in long-term rebuilding programs, either. Gibbs is well aware that not many fired coaches get second chances.

Certainly, Gibbs is behaving like a man who is confident he will never have to send out his resume.

If he is experiencing growing pains, he's keeping them hidden, except for an occasional swipe at the team's press coverage. There are no signs of hesitation in his commands, no evidence of leadership frailties. He relishes the idea that, after so many years of having someone else make the final decisions, the buck finally stops at his clipboard.

Gibbs is a product of the new wave of boy wonder assistants in the NFL. Lombardi cast off his clones, then Shula bequeathed his. Now Coryell, the Don of San Diego, is distributing his air force graduates throughout the league.

But Gibbs is trying to be different. He wants to be a rare head coach who doesn't relinquish the informal ties he developed with players as an assistant. He wants to be open and friendly yet maintain the necessary discipline and to command respect.

"So far, I've been very impressed with him as a person as well as a coach," said safety Mark Murphy. "He's an optimist but not to the degree where he is blind to reality. Players appreciate that. We aren't going to be suckered in by fantasy talk.

"He's very outgoing, which is a change from Jack Pardee, who was really a shy man. It was hard for players to go in and talk to him. Gibbs says his door is always open and he seems easy to talk to, at least in the contact I've had with him. You have to be able to go to a coach with the knowledge that what you say to him with stop there."

Gibbs prides himself on being a players' coach who maintains a practical approach to football. Away with physically punishing drills. Be gone with endurance-test practices. So what if his meetings run too long and his obsession with films becomes overwhelming, as long as his workout philosophy, at least in the athletes' minds, will preserve their legs and endurance for the regular season.

"You don't go to your room at night and say, 'Oh, no, I got to get up in the morning and run those damn striders,' " said quarterback Joe Theismann. "He uses common sense. How many times can you say that about a coach?"

Not that Gibbs is Mr. Bubbly and no burst. He'll flare up at lackadaisical play and botched assignments. He's demanding and impatient with ineptness. Break one of his rules, show indifference to his team unity concept, and beware of his wrath. Just ask Jeff Williams, exiled in San Diego, or Coy Bacon, fined in Carlisle.

"He's a great believer in perfection," said Terry Metcalf, who played under Gibbs at St. Louis. "He'll get upset when you make mistakes on things that you have down pat. He'll raise his voice, but later he'll almost be apologetic about how he acted. I think people are realizing he can be their friend if they let him."

So far, he has charmed this team as much as any coach can charm skeptical athletes before they've endured even one regular-season game. Players are the original show-me types. They'll have lasting faith in any system that will produce wins and playoff rewards.

But how can you bet against someone like Gibbs, who could be the original All-American Boy? God-fearing (a born-again Christian), natural athlete (former national masters racquetball champion), family man (two sons, charming wife). Even the players he cut in training camp were hard-pressed to criticize him, mainly because he hasn't conceded yet that his profession is harsh and that a head coach should function without emotion or feelings for his athletes.

"I really agonized over making the cuts," he said. "I wanted to give everyone an even break. I didn't want them to think they were overlooked. When you like people, letting them go isn't easy."

Gibbs was noticeably depressed on cut days. But he doesn't lack a sense of humor. He's a whiz at telling stories, which makes him a highlight of any party even though he doesn't smoke or drink. He also has a touch of eccentricity. He gets so wrapped up in his Xs and Os that he forgets appointments, phone calls, even practice times -- a sort of absent-minded professor of football.

"It's always seemed that Joe would eventually be a head coach," said Wayne Simmons, Gibbs' best friend and the Redskin tight end coach. "It was something we all took for granted. And no one ever thought about him failing. You are around someone long enough you get to know them. He just has what it takes to be one of the best."

Before Gibbs can be enshrined in the Hall of Fame, however, he has to translate his glowing tributes into on-the-field success. Others before him, like Phil Bengston, Forrest Gregg, Howard Schnellenberger and Bill Arnsparger, have come into head coaching jobs with impeccable assistant coaching credentials, only to fail. No one is sure how Gibbs will react to losing, or how he will cope with the pressure of constant decision-making.

"I don't spend a lot of time worrying about how I will do," Gibbs said. "I feel comfortable in this job, I haven't felt like I've gone through a transition at all. All you can do is work as hard as you know how and prepare the team the best you can.