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Why do we need an angle system other than degrees? Why are there even other angle systems? What is a radian anyway? Why do we need radians? Where did the idea of having 360 degrees in a circle come from? All of these questions (and more) and answered in this video! This video looks at what a radian is and why would need it when we have degrees. I look at the unit circle and how we can use it to define what a radian is and then look at converting between radians and degrees. Passing through the idea of notation there are then a number of worked examples where we convert between degrees to radians and radians to degrees. There is also the usual MaffsGuru humour - which is generally not funny - but spends rather too long asking for people to subscribe. This is needy maths! Hope you enjoy it!
One of the most hated subject in Mathematics seems to be the Unit Circle. It seems that once student shave been taught it, they equate this to something close to worshipping the devil. They try and avoid it at all costs!!!! This video is here to make the topic as easy as it can be! And I have to admit to really loving teaching the unit circle. It starts by recapping the work on degrees and radians. This is good! Normally at this point, teachers would then dive straight into the Unit Circle. I don't. I take a look at Sine and Cosine Curves. Using the CAS I sketch the curves and then take the time to explain how this can be mapped onto this thing called the Unit Circle (which ... to be honest ... is nothing more than a circle with a radius of one unit!). Once we understand how the Unit Circle is created, I do a number of examples of how to use it with reference back to the Sine and Cosine curves. I guarantee that, when you watch this video, you will understand the sine and cosine curves with relation to the Unit Circle. If you don't understand ... this video comes with a money back guarantee. Which is awesome ... as the video is free!
And so the excitement continues! With this, the third video in this series which looks at the Unit Circle. Where does it come from? How do we use it? Why do we use radians? What's the point? All of the above are really good questions which this video, alongside the others, will hope to answer. This video, like the others, uses the Unit Circle to scaffold the learning. We have already dealt with Sine and Cosine. We use this understanding to help us work out the Tangent of common angles using the Unit Circle. Bucking the trend, I once again take some time to look at what the function looks like using the CAS calculator before referring this back to the Unit Circle. There are cheesy puns, Dad jokes and lots of jokes about the price of fish .. and a possibility of me eating KFC! I do all I can to make the MAths interesting and understandable in with a liberal dose of humour. I hope you enjoy it!
I love everything to do with the Unit Circle and this has to be my favourite lesson of all time. The beauty of the symmetry properties of circular functions never fails to impress me. In this video sit back and enjoy as I take you on a journey of learning and discovery about the unit circle. Looking at the construction of the Unit Circle and how we can relate angles to the length of horizontal and vertical lines doesn't sound very easy, but I take time to explain the concepts in an easy to understand way. I look at all the identities which are created from the Unit Circle and then explain how they can be used with the ASTC notation to help you find the size of any angle between 90 and 360 degrees if you know the size of an acute angle int he first quadrant. I look at a number of questions and show how they can try and trick us!
This video looks at how to find the exact values of common angles using the two triangles. This is one of the most awesome ways of doing maths. If you don't understand this by the end of the video then I've not done my job properly! Once we have worked out how to use the two triangles to find the most common angles, I then take time, using examples, to show you how you can combine your understanding with the work done in previous videos on the Unit Circle. This is the most fun you can have in Mathematics. I promise ... or your money back!
This is a topic which, without fail, appears on every known exam. Well ... so long as it deals with trigonometry! I take some time to look at why, when we have trigonometric equations there is more than one answer using various graphs. Knowing there is more than one solution, I look at how we can use the two traingles, then the unit circle and some good old fashioned calculator use to find all the missing angles both with degrees and radians. I even look at how to decode the general solution when you dont limit the domain. Complex examples are studied and full worked solutions explained. This is the most comprehensive video I know which explains how to find all the solutions to trigonometric equations. I hope you enjoy watching it. Let me know if there is anything you don't understand.
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These are the videos which are available in each chapter. You will notice that some are free and some are for subscribers only. Making and hosting these videos costs a little bit of money. To help pay for the hosting fees I have no choice but to hide some of the videos and make them for subscribers only.