Category Archives: Math-11

Pre-Calc 11 Top 5 for 2017

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  1. Do assigned homework as soon as its assigned

The worst thing that you could possibly do is leave your homework to the last minute. You will have so many question’s and I can guarantee that you will realise you don’t know even half of what you thought you did (trust me I have been there, done that).  Your tests also become so much less stressful and easier for you if you do all your homework on time.

  2. Use class time wisely

If you use your class time wisely, not only do you not have to do as much homework at home but you also have people there to help you if you get stuck. You may want to relax and not do anything, but why do that now, when you could do that later instead of your homework! Furthermore, this will help you to stay on track with completing assigned homework as soon as it is assigned.

   3.  Don’t prepare for tests the day before

This can go hand in hand with not completing your homework on time, but there is nothing worse than studying the day before! You will not have time to ask questions the next day if you get stuck on one, therefore you will be at a huge disadvantage and your grade will suffer from that. And who wants that!?!?!

   4.  Write notes

Notes can help you for your assignments for that day, for unit test, but most especially for the midterm and final. They are so easy to go back to if you forget how to do something. Notes will be your holy bible of Pre-Calc 11!

  5.  Focus from the beginning to end

Whether it is the start of the year or the end of it, everyone will begin their semester off trying their ultimate best. Though, we all know that we say to ourselves “well if I don’t study for this test, I’ll just study for the next one”. That right there, not a good plan, because one test can affect your mark and learning severely. Everything we learn in Pre-Calc all coincides with each other and if you miss out in learning for one or two units everything else will not make sense. So listen, do your homework and don’t tell yourself that you’ll start trying again near the end of the semester because by then, it is already too late! You only have one year left of school after this, make it the best that you can make it!

When to use What Trig

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Basic Trig Identities: You only can use basic trig when there is a triangle with a right angle and the necessary information.

There needs to be a right triangle because there needs to be an hypothenuse. Furthermore basic trig consists of Sine, Cosine and Tangent, which is also SOH, CAH, TOA. A trick used to know what side (opposite, adjacent, hypothenuse) of the triangle is needed to figure out the angle (vice versa).

Look at this example…….       We knew the angle F (38*) and the side FD (10 cm), which is also the hypothenuse. Meaning that we can use the formula CAH to figure out the side ‘d’. We put the given numbers into the equation, rearranged it  and then we were left with the answer (7.9 cm)  to the adjacent side of COS 38*.                  

Sine Law Identities: You can only use sine law if you have a non right triangle and atlas on of the angles and their opposing side of the triangle.

The sine law equation looks like this… Sin A / a  =  Sin B / b  =  Sin C / c   …. Meaning that the angle of A divided by its opposing side (side a) is equal to angle of B (or C) divided by opposing side b (or side c).

Take in this example…..  It is NOT a right triangle but we do know the angle of G and its opposing side g or known as JH (10 cm). We also know side h or known as GJ (15 cm) but what we do not know is angle H. So what we can do is punch all our given answers into the above sine law equation, rearrange it, to then come to our answer which we will invert sine it, to finally get the real answer of angle H (34*).

Cosine Law Identities: Cosine law can be used for any type of triangle but ONLY ones that have a contained angle and information limited enough, that it is impossible to use the sine law. 

The Cosine law equation looks like this…. c*2 = a*2 + b*2 – (2ab cosC)  ….. This equations is used if there is not a given answer for an angle AND its opposing side length, because with that information you can use sine law. However, without it, you need to use cosine.

Look at this example…. Immediately we can see that there is a contained angle (an angle that is “cornered” by a length of a side on both sides of it). We can also notice that there is limited information, so the sine law will not work and it is NOT  a right triangle so the basic trig will not work either. Therefore we will take the oscine equations up above and bunch our given information into the equation and we will come out with out finally answer (6.3 cm).

In grade 10 I only knew the basic trig identities, which were useful but if it was not given enough information or if it was NOT a right triangle I would have to do so much extra work (ex/ splitting the triangle into two). Though, now in grade 11, with the sine and cosine law, I do not have to do as much work as before because I have the knowledge to do steps that I did not know how to do before.