Can someone help me out? I’m studying for my test tomorrow, and I get it for the most part. I’m just confused on a couple of things. I understand how my teacher got all the way to the sinx = -root 2 over 2 but how did they get 5 pi over 4 + 2n pi and 7 pi over 4 + 2n pi?

Titus works at a hotel. part of his job is to keep the complimentary pitcher of water at least half full and always with ice. when he starts his shift, the water level shows 4 gallons, or 128 cups of water. as the shift progresses, he records the level of the water every 10 minutes. after 2 hours, he uses a regression calculator to compute an equation for the decrease in water. his equation is w –0.414t + 129.549, where t is the number of minutes and w is the level of water. according to the equation, after about how many minutes would the water level be less than or equal to 64 cups?