To find the derivative of sin(x), they drew tangent lines to sin(x) (printed out on paper), measured their slopes and then graphed the derivative point by point. Here’s a desmos version.

From that derivative fact and noticing that the derivative of cos(x) is -sin(x), they have enough to find the derivatives of tan(x), csc(x), sec(x), and cot(x). Let them at it.