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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 had the privilege of being one of Graeme’s students in 2005. As a creatively minded individual I struggled greatly with Mathematics and was falling behind in my HSC studies. Under his careful and creative tutelage I began to truly understand Mathematics for the first time in my life. Graeme patiently taught me to master mathematical concepts in ways I could understand. In the week intensive I spent with him he taught me the entire HSC course, and I went on to receive a Band 6. I cannot recommend him highly enough.

Roxanne G (student, 2005)

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