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How to Sketch Trigonometric Functions

Graph of the sine functionGraph of the cosine functionGraph of the tangent function

Learn to sketch your basic three functions first.  My first video (below) will show you what to do.

You will then learn how to interpret changes to the basic function, and what that means for a graph.  For example, if you know how to graph y = sin(x), in time you will learn how to “read the clues” and graph y = 3sin(2x – 90°) + 1 [or y = 3sin(2x – π/2) + 1 using radian measure].

There is another way of understanding the effects that the extra numbers have on functions, and that is to learn how to identify a complete wavelength or cycle.

In time, I will be adding material to show you how you graph trigonometric functions using BOTH methods.

How to Sketch the Three Key Trigonometric Functions in 20 Seconds Each

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.

I have been watching your “Integration technique” videos with high expectation and excitement. They never fail to give me a lot of joy and much pleasure. You must have been one hell of teacher at your time! … just continue making highly enjoyable and intellectually stimulating videos. … Unfortunately, what you learn at the university, you hardly ever see again in your office job. That is why I try to repeat some thing I learned: to enjoy it a bit more, to marvel upon beauty, and to keep my brain sharp. There is where your videos come in perfectly: interesting, amusing and thought provoking problems neatly presented. … You do your best to share your passion, knowledge and experience. The least I can do is to say an honest “Thank you!” As I said, your videos give me much pleasure. You may freely let other people know that. … Rest assured that I shall be watching your videos in the future. With joy and excitement. And I shall comment on them from time to time. You just continue making them.
Zoran V (in private correspondence via YouTube, quoted with permission)

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