I am teaching a Pre-Calculus course - I've taught pre-calc before, but at a different school, and the scope is different due to what they've learned in previous years. I have a background in math, and my content-knowledge is very strong, so I often don't use any reference materials for myself when creating my lessons. It has never been a problem, until now. I taught something incorrectly (we are graphing trig functions, and for secant and cosecant, I thought they would just take the reciprocal of all of the y-values for either cosine or sine). I just didn't take enough time to clearly think it through and was trying to quickly get my lesson done. My mistake. How do I handle it with the students? When they checked their homework from Thursday night it didn't match up with the answers in the back of the book, and so they told me on Friday. I told them I would give it some thought and see what is going on. Obviously I need to reteach it. But I'm worried about losing my credibility with them. This is my first year at this school, so I don't even have a solid reputation to bank on. They need to trust my content knowledge, but these students are at a very high level and I'm worried that I'll lose all of their respect and that they'll never take me seriously again.