Cogan made his Indycar debut at the 1981 Indianapolis 500, driving for Jerry O'Connell Racing and finishing fourth. Despite this result, he lost the Rookie of the Year Award to Josele Garza. He then competed in the rival CART/PPG World Series for O'Connell, achieving a second-place finish at the Milwaukee Mile in his debut.
In 1982, Cogan joined Team Penske, earning a third-place finish at Phoenix International Raceway and a second-place finish at Pocono International Raceway. He secured pole positions at Cleveland and Riverside, finishing sixth in the championship while teammate Rick Mears won the title.
The 1982 Indianapolis 500 was marked by a controversial incident during the start. Cogan swerved into A.J. Foyt, collecting Mario Andretti and damaging the cars of Dale Whittington and Roger Mears. Bobby Rahal also reported being hit. Andretti expressed his displeasure, stating, “This is what happens when you have children doing a man's job up front.” Foyt added, “…he ran right square into my goddamned left front… ‘Coogin’”. Gordon Johncock later suggested the polesitter, Rick Mears, brought the field down at a slow pace, while Foyt, in a 1983 memoir, assigned some blame to Mears but primarily to Cogan. Cogan finished 47th in the USAC Gold Crown season points due to a technicality regarding his USAC license.
Following the incident, Cogan faced a "blacklisting" by fans and press. In 1983, he drove for Bignotti-Cotter Racing, achieving a fifth-place finish at the Indianapolis 500. He finished 15th in the CART standings and 6th in the USAC standings.
In 1984, Cogan drove for Curb Racing and All American Racers, setting a speed record for stock block engines at Indianapolis, but retired after 137 laps with a frozen wheel. A crash during practice for the Pocono 500 resulted in broken heels and a torn Achilles tendon, ending his season.
Cogan drove for Kraco Racing in 1985, finishing 11th at Indianapolis and 14th in the championship. He joined Patrick Racing for 1986, scoring his only Indycar win at Phoenix and finishing second at Indianapolis, leading for a time before being passed by Bobby Rahal.
For 1987, Cogan returned to Patrick Racing, but achieved only a pair of fifth-place finishes, ending the season 16th in points. In 1988, while driving for Machinists Union Racing, he was injured in a crash at Toronto, missing four races. He finished 13th in points.
The 1989 Indianapolis 500 saw Cogan involved in a significant crash, escaping unharmed from a car broken in half. In 1990, he drove for Vince Granatelli Racing and Stoops Racing, finishing ninth at Indianapolis. A serious crash at the 1991 Indianapolis 500, involving Roberto Guerrero, resulted in a broken femur and other injuries, sidelining him for the remainder of the year. Cogan’s final season was 1993, driving part-time for Galles-Kraco Racing, finishing 14th at Indianapolis.
Since leaving racing, Cogan has distanced himself from the sport, focusing on a real estate business in Los Angeles. He declined interviews for the Indianapolis Motor Speedway centennial celebrations in 2009 and 2011. In a 2015 interview, Cogan noted lingering pain from his racing injuries. He is married with two sons and a daughter.
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