I am convinced that students can learn to graph each of the three functions (sine, cosine and tangent) in 20 to 30 seconds. I am also convinced that if a student will take the time to develop this skill, it cannot fail to enhance his/her understanding of each function and its behaviour. These curves are so useful and so much a part of the foundations of trigonometry that I think all serious students should master this graphing skill.
So, in this video I lay down a challenge! I challenge you to sketch the sine and cosine curves in under 20 seconds and the tangent curve in under 25 seconds. The video below will explain how to graph the three curves.
Actually, I recommend more than that. When learning this material, spend 60 to 90 seconds drawing all three functions before starting your trigonometry homework ... especially conversions between sine and cosine functions, finding exact ratios for angles of any size, and graphing more complex trigonometric functions.