Weektask 2 solution of trigonometric equation

 

                                             this was the question I have module there.

It’s pretty much easy to do if you could look at this with a quiet different angle. I have shown each of them by breaking them in to three pieces. This is too difficult to go through usual methods. Usually students use to get some substitution on inverse terms to make them easier. But at this moment those usual substitution just like three of them are going to equal with three different parts such as alpha, bita and gamma will not help you to reach for the solution easily. That’s not impossible but it becomes much more complicate and takes much time. If you pay attention on those angles very carefully you may able to see that right hand side is nothing else the expansion of sin2^n. I have given there pi notation also that is nothing else which stands for the multiplication just like summation. Most appropriate substitution for the right hand side is introduced as mention in calculation. If you are familiar for those plain trigonometrical expressions it’s not too hard to find out it. So keep doing it with them no need to explain others up to final stage coz I’m pretty sure that you may able to complete it now.       It’s pretty much easy to do if you could look at this with a quiet different angle. I have shown each of them by breaking them in to three pieces. This is too difficult to go through usual methods. Usually students use to get some substitution on inverse terms to make them easier. But at this moment those usual substitution just like three of them are going to equal with three different parts such as alpha, bita and gamma will not help you to reach for the solution easily. That’s not impossible but it becomes much more complicate and takes much time. If you pay attention on those angles very carefully you may able to see that right hand side is nothing else the expansion of sin2^n. I have given there pi notation also that is nothing else which stands for the multiplication just like summation. Most appropriate substitution for the right hand side is introduced as mention in calculation. If you are familiar for those plain trigonometrical expressions it’s not too hard to find out it. So keep doing it with them no need to explain others up to final stage coz I’m pretty sure that you may able to complete it now.       

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Sin rule constant (plain trigonometry )

 In this section i hope to give you an idea about sin rule which is related to plain trigonometry . I have seen that so many students use to call this as a constant but they don't have the proper idea. It should be done even each of every definitions should be known with their geometry. Not only sin rule even we can interpret other geometrical properties of triangles and polygons. Even you guys should be able to derive each of every equations and relationships with geometrical figures. This is shown only for an ordinary triangle but this should be proved for other two sceneries too. Hope you may construct them for others too. That's pretty much easy to derive with projections. Exactly this constant equals to the reciprocal of diameter of it's own circum-circle. It means the constant is unique for the corresponding plain triangle. And also I have tried out to show you how sin ratio can be calculated in terms of sides of triangle. In our old syllabus all these were taught but I would like to ask what happened to them. No need to be framed or trapped in side of a single margin .as well as each of every ratios can be computed. If we could apply s=(a+b+c)/2 expressions can be concluded so far. I just invite you guys to appreciate this. Basic mathematics factors are used.