Raise a glass of holiday cheer to “Hidden Figures,” the “Rocky” of math movies. You might just find yourself applauding during certain moments of dramatic triumph in Theodore Melfi’s unabashedly sentimental and wonderfully inspirational film, and yes, some of those moments feature people working out high-level math problems. Not just any people, but some key figures — and yes, some hidden figures — in NASA’s heroic effort to win the space race against the Russians in the 1960s. Based on the non-fiction book by Margot Lee Shetterly, “Hidden Figures” shines a deserving spotlight on three black female mathematicians working for NASA in the computers division at the Langley Research Center. — Octavia Spencer is Dorothy Vaughan, who does the work of a group supervisor, but is thwarted in her efforts to get the title, the pay and the recognition of a supervisor. Her smug and condescending boss (Kirsten Dunst) clearly believes an African-American woman shouldn’t be elevated to equal status. — Janelle Monae is Mary Jackson, an aerospace engineer who literally has to take her case to court so she’ll be allowed to take night classes to pursue an advanced degree. Spencer and Monae deliver beautiful, strong, immensely effective, nomination-worthy supporting performances. — And Taraji P. Henson’s Katherine Johnson is at the front and center of the story, as the lone African-American woman working in the vital Space Task Group, the NASA engineers charged with mapping out America’s manned spaceflight programs. Playing a character about as far away from “Empire’s” Cookie as the acting spectrum will allow, Henson delivers the performance of a lifetime. She disappears into the persona of the bespectacled, nerdy, determined, confident, pioneering Katherine, who has to fight to have her ideas heard, has to fight to even get a seat in the room where all the key decisions are made, and even has to fight for the right not to have to run halfway across Langley every time she has to go to the bathroom because the ladies’ room in her building is for “whites only.” Co-writer and director Melfi (who directed the equally sentimental and quite terrific Bill Murray vehicle “St. Vincent” a couple of years ago) announces the borderline corny tone of “Hidden Figures” from the get-go, with Mary, Dorothy and Katherine stranded after their car breaks down. A squad car with lights flashing pulls up, and a white state trooper approaches the ladies and asks for identification. When Katherine shows him her NASA badge, the officer exclaims, “NASA! I had no idea …” “There are quite a few women working in the space program,” says Dorothy. After the car is fixed — Dorothy susses out the problem — the trooper gives the ladies an escort, and Mary quips, “Three Negro women are chasing a white police officer down the highway in 1961. That is a God-ordained miracle.” We get a number of scenes with a similar vibe in “Hidden Figures,” with the women dealing with long-standing stereotypes and subtle (and sometimes not-so-subtle) racism. Most of the white characters in the film are basically good people who come to see the light about their prejudices. Kevin Costner has the Kevin Costner role as Al Harrison (a composite character), the crusty head of the Space Task Group, who goes about his business like Vince Lombardi — barking at his team, telling them they’re losing to the blasted Russians and they better GET WITH IT. Glen Powell is John Glenn, who doesn’t care about gender or color; he just wants the smartest people available to calculate his path, because HE’S the one going up in that capsule. Mahershala Ali is his usual welcome presence as Jim Johnson, the military man courting Katherine (and her children). Katherine’s so focused on her career she almost has to be reminded she’s falling in love. But mostly and most memorably, “Hidden Figures” is about Katherine, Dorothy and Mary, three remarkable and groundbreaking American heroes. Henson, Spencer and Monae are all so good. Each has her individual moments, and they’re wonderful together, even when we get cliched scenes such as the obligatory “everybody dances in the living room” routine. Katherine’s glasses don’t hide the unwavering look of determination in her eyes. Dorothy knows exactly how and when to play her trump cards to get what is rightfully hers. Mary’s speech to a Virginia judge in which she appeals to his ego so he’ll rule in favor of her breaking the color barrier in night school is a pure applause-inducing moment. Junior high and high school classes across the country should take field trips to see this movie.