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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 would describe Graeme as one of the best tutors I ever had. During my school years I spent some time attending one of the major tutoring organizations in town and I found it was difficult for the tutors to spend the time needed to assist me with problem solving due to the class size. My mother rang a private tutor in the phone book who gave her Graeme’s phone number as he specialized in tutoring high school students and was a teacher who used to work at my school. He offered a tutoring service at convenient times which suited our busy life style. The one-on-one service that Graeme provides was what I needed and I saw improvements straight away with my exam results. This made my parents very happy and I found a new confidence in approaching exams. I have since left school but have stayed in contact with Graeme and he has provided me with terrific practical suggestions in preparing for interviews. I would not hesitate in recommending Graeme as a great teacher.
James C (Student, 2012)

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