What is a tangent? Is it a ratio of sine to cosine?
Your question is confusing me too! I think you are confusing the two meanings of “tangent” in mathematics: 1) In geometry, it’s a line touching (not cutting) a curve, such as a circle. 2) In trigonometry, tangent of an angle ¢ is the ratio (sin¢)(cos¢). “Draw a tan theta touching the circle” seems to muddle these two. Does that help?