Imagine you are flinging a yo-yo in a circle around your head. You let go, and it flies off in a straight line towards your mom’s favorite ceramic figurine.
Tangent lines have caused you grief, yet again. In this case, the tangent is the line formed by the yo-yo point of release to the point of impact. A tangent is a straight line that has the same slope of the point it’s touching. They’ll show up most often when we talk about slopes and derivatives. Yes, you also saw these in trigonometry and geometry.