Ah, say I, rubbing my hands ingratiatingly, May I interest you in - TopicsExpress



          

Ah, say I, rubbing my hands ingratiatingly, May I interest you in a little bit of trigonometry? Well, perhaps I dont need to be quite so Uriah Heepish (you might detect that I have read some Dickens). What I have to share in the next four videos is a very graphic and logical way of illustrating, understanding and learning the four fundamental identites that we use in trigonometry. What is contained in THIS video is related in every trigonometry textbook in one form or another. The following two videos, however, should be very new to you and help you quite a lot. Think of this video as establishing the foundation for the others ... When we first learn trigonometry, we learn how the ratios relate to the sides of a right-angled triangle. By placing such a triangle within a circle (with a radius of one unit) on graph paper, however, new definitions emerge. I show what these new definitions are and how to understand them geometrically. With practice, you should be able to estimate the sine or cosine of any angle up to 360 degrees IN YOUR HEAD with reasonable accuracy (within a decimal point or two). It is good to practise this skill. You can do so with a friend who can check your results on a calculator. I then show how this new understanding gives rise to two of the four key identites ... tan(θ) = sin(θ)/cos(θ) and the first Pythagorean Identity, sin²(θ) + cos²(θ) = 1. At the conclusion of the video, I explain how you can quickly learn the pattern/diagram and the two identities. It just takes a minute or two each day for a few days. This new understanding means that we have now broken free from the confines of right-angled triangles. We will soon learn how to use these definitions to analyse triangles of any shape! The new understanding from the unit circle also meant that mathematicians discovered that they had the tools to analyse wave motion and the motion of anything that oscillates or wobbles or moves in a repetitive way. What a revolution! I hope you enjoy these first steps along that journey.
Posted on: Sat, 01 Nov 2014 15:32:51 +0000

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