I had a similar experience in eighth grade with introduction to trigonometry. The teacher put in 0, 30, 60, 90, ... on the x axis and sine (x) on y. Then they

I had a similar experience in eighth grade with introduction to trigonometry. The teacher put in 0, 30, 60, 90, ... on the x axis and sine (x) on y. Then they began to join them with a beautiful curve. I protested and inquired how we can just join those dots seemingly on faith. The teacher just ignored me in spite of my repeated protests.