At a high-altitude observatory, Emek and Tara prepared to measure an exoplanet as it passed in front of its star. During the eight-hour observing period, the star's apparent angle above the horizon was modeled by A(t) = 25 sin(πt/4) + 45, where t was the number of hours after 8:00 p.m. The clearest measurement would occur when the star was at 57.5 degrees. Setting A(t) = 57.5 gave sin(πt/4) = 0.5. Tara used the sine relationship to find two solutions within the first cycle: t = 2/3 and t = 10/3 hours. That corresponded to 8:40 p.m. and 11:20 p.m. However, the telescope could not operate below 60 degrees before 10:00 p.m. because a nearby ridge blocked part of its view. The first solution was therefore unusable, even though it satisfied the equation. Emek checked that the later time occurred after the restriction ended. They scheduled the observation for 11:20 p.m., aligned the telescope, and successfully recorded the exoplanet's transit.
