This week in Pre-Calculus, I feel we went much deeper into trigonometry. We learned a lot of new concepts and one thing in particular I liked was special triangles. Special triangles help you find the angles (rotational and reference) when working with different trig problems.

These are my notes and I’m going to explain them so excuse how messy they are. At the top, you can see two special triangles. Pretty much you can have triangles with 30, 60, and 90 angles or you can have 45, 45, 90. These set of angles can help you determine what kind of triangle you dealing with and help; you figure out your rotational angle and the side lengths on your triangles.

Triangles with angles 30, 60, and 90 will have the side lengths 1, root 3 and 2

Triangles with angles 45, 45, and 90 will have the side lengths 1, 1 and root 2

The reason I like these triangles is because when doing questions with them you automatically know your side lengths just from the angles. It makes questions that seem hard quite simple!!

This week, in pre-calc 11, we started our trigonometry unit. We mainly worked on reviewing from grade 10, but even this I wasn’t very confident in, as the last time I reviewed trig was the first semester of grade 10. Once I started to practice questions, it jogged my memory a little better, and I was beginning to remember the concepts practiced last year.

The question I made the most mistakes with is number 8. I was very confused about where to start and what I was meant to do. Once I understood that I was just looking for the missing variables it was very easy as you’re just plugging the numbers into your calculator. First I found side A. I did this by taking the opposite side and dividing that by Tan38 which is the numbers needed as you’re using the opposite and adjacent sides. 38 is your angle so that goes with the ratio you are using. Then I used those two sides to find the hypotenuse. This was quite simple as you can just use A^2 + B^2 = C^2. Finally, I used the two angles to find the missing one. Since we know that all the angles have to add to 180 degrees in right triangles this is quite simple. All I had to do was minus 90 + 38 from 180 and that gave me the answer of 58 degrees.

That is how I solved the sides of this triangle.

This week in Pre Calc we did our final review on rational expressions and equations as we have our unit test on Wednesday. the mistake I wanted to look over this week was on the skills check we did on Thursday.

At first, when doing this question I made a mistake when factoring. It’s important to look over your work cause a simple mistake while factoring can mess up your entire answer. I factored using -8 and 3 instead of -9 and 4. Factoring an expression like this is nothing new and something I’m capable of doing but I made a simple error by just guessing and not checking to make sure those numbers fit the expression and that completely changed my answer. In the end, I caught my mistake and redid the question. Another thing is I forgot to do my non-permissible values. It’s smarter to do these before solving the expression as these values relate to the beginning values.

This is how I ended up solving it. Since it’s a division question I factored everything and then used the reciprocal of the second expression and multiplied everything. This question isn’t difficult but a simple thing like factoring can really change your answer which is why it’s important to not rush and look over your work.

This week in Pre Calc 11 we started learning about rational expressions. These were very similar to solving fractional expressions and the rules were very simple as well. I wanted to talk about adding and subtracting in specific. When adding fractions the main rule is that you have to make sure they share a common denominator. When doing this with regular fractions you can easily find one but with rational expressions it can be a little more difficult.

Let’s use this equation as an example. You have to 3 + 2 over two factorable expressions. The first step is to factor these expressions into the simplest form. this gives you (t-2)(t-5) + (t-2)(t-4). Now you can look at what they have in common. Sometimes they won’t have something in common but here they do. That means that each side’s numerator needs to be multiplied by what they don’t have in common. 3 will be multiplied by (t-4) and 2 will be multiplied by (t-5). Now they multiply the denominator by the same numbers so they become common. Your new denominator becomes (t-2)(t-5)(t-4). You only need to write t-2 once as that’s their common factor.

Now, you can simplify the numerators and cancel out anything common in the denominator and numerator. In this example, once you simplify the top, you get t-2, which cancels out with the bottom. In the end, you’ll get 1 over (t-5)(t-4).

that’s your final expression but you’re not done yet. You have to write your non-permissible values. These values are the ones that won’t make the denominator equal to 0. In this case it’s T can’t equal 2,5,4. Always get these values from the original equation as things simplify and cancel out throughout the equation.

That’s how to add/subtract rational expressions.

This week in Math 11, my best mistake happened during our previous skills check. I know we did it a while ago, but I redid it while studying for the midterm. I originally had trouble with it and was still struggling while trying again. I specifically didn’t understand how to find the function of a parabola by looking at a graph.

For question 5 I didn’t know that by just finding the vertex you can find the whole equation for vertex form. Pretty much look at your parabola and see where the vertex is. Once you find the vertex, input that into your equation and make sure to check for a stretch by looking at the line of symmetry. This goes either way with graphing. It was a lot easier when I figured it out but once you figure it out it’s much easier than you’d think and can help you with a lot.

This week in pre-calculus, we elaborated more on quadratics and began graphing with them. We learned a lot about graphing different things and some new vocabulary. I was a little confused by the end of the week but after reviewing my notes and going over some different concepts, it’s becoming much easier.

We learned about the 7 most important things when graphing. These include:

1. X intercept
2. Y intercept
3. Domain
4. Range
5. Vertex
6. Line symmetry
7. 1,3,5

These help you understand graphing a little better, in my opinion. The first thing we worked on this week that I struggled with the most was a very simple concept. It was just graphing with T charts. I hadn’t graphed since year so just wasn’t understand how to do it when you add in different variable to the equation.

I’m gonna use the first one as an example. Y= 2X^2. This is very simple with a t chart. You just make a list of X values (-1,-2,-3,0,1,2,3 being the easiest) and input them into the equations.

Example is 2X^2 = 2(1)^2

The answer would then be 4, and then you have your Y value for graphing. After reviewing this, it was quite simple; it just took me a second. I enjoy this class as I feel like I can just use the base concepts I’ve learned in math throughout the years without having to learn any crazy new concepts. Eveerything seems to link back to the foundations we learned.