This week in PreCalc 11, we learned about the Sine Law in Trigonometry. The Sine Law is a law to help more easily determine the angles/sides of a given triangle. When putting this law into practice during homework questions I was unaware that
Sin A/a = Sin B/b = Sin C/c was used to find the angles
while,
a/Sin A = b/Sin B = c/Sin C is used to find the sides of the triangle
As you can see in the first image, Sine Law is used to find the angle with Sin A/a = Sin B/b = Sin C/c
And in the second image Sine Law is used to find the side length with a/Sin A = b/Sin B = c/Sin C
This week in PreCalc 11 we started Trigonometry. The mistake I chose to focus on for this week was the mistake I made when finding the reference angle. I chose this mistake because I did it multiple times. When finding the reference angle you take the rotational angle and either subtract or add it to the closest x-axis. When doing this I would so often subtract or add it to the number from the y-axis.
This week, in pre-calc 11, we started our trigonometry unit. We mainly worked on reviewing things we learned from grade 10, however my confidence in the review was low as well. Once I started to practice questions,I was reminded how to do some questions 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.
This week in PreCalc 11 we learned about multiplying Rational Expressions and Equations. When multiplying Rational Expressions and Equations, the same rules when multiplying fractions apply. You can multiply across but there are ways to get answers quicker. A lot of the time when there are rational expressions and equations, they can be factored/simplified more to make it easier for you to solve. My mistake this week was not simplifying as far as I could.
For example: in this question, you have to factor everything, then cross out the like terms. When I did it I did not cross out the like terms but just tried to multiply everything across, which didn’t work. I then was shown that when finding the like terms I can just cross them out which simplifies the equation so much more. Then it was just placing the left over terms together/ over each other/in fraction form and doing simple reducing and division. Then I got the right answer.
This week in PreCalc 11 we learned how to divide rational expressions. When dividing rational expressions, the first step to ensure you are getting it the simplest form you can before anything else is to make sure the equation is fully factored. When completing a question in the book I did that, and made sure it was as simplified as it could be. However, to simply complete a division question like that, you can flip the second equation you are dividing by and just change it to a multiplication question, which makes it easier for most people doing the questions.
Then, you cross out common factors and state ALL the Non-Permissable Values. Then the question is finished.
This week in PreCalc 11, we learned about finding the Non-Permissable Value in a Rational Expression/Equation. To do this when given the equation you have to, first of all, simplify/factor the farthest you can before trying to find the Non-Permissable Value. This way you can see if you can cross out any matching pairs.
However, you still need to find the Non-Permissable Value for that pair, because there is a Non-Permissable Value for every denominator (NPV’s only apply to the denominator). Therefore in the example the NPV is x ≠ -10 because both of the fully factored equation on the denominator is (x + 10) and you are just solving for x so -10.
However, my mistake for this week is that when I was solving for the Non-Permissable Value/X I did not switch the sign when switching it to the other side to solve for the x.
This week in PreCalc 11 I learned about graphing inequalities. My mistake of this week was when graphing the equation x^2 – 5x – 6≥ 0. It is factored into (x-6) (x+1) ≥ 0, I didn’t understand that you switch the signs for the x intercepts when graphing them.
A mistake I made this week that helped me learn while reviewing for my midterm was when rationalizing the denominator. I wasn’t aware that when rationalizing the denominator in a question like :
5√5/4√5
I did not keep the 4 connected to the √5 when multiplying the top and bottom by the conjugate which is wrong. Therefore I got the wrong answer. Instead I should have multiplied both by 4√5 resulting in the top of the equation being:
This week in Math 11 I learned about Quadratic Functions and Equations. My mistake of this week was while factoring 80x^4 – 5. I got to factoring it to 5(16x^4 – 1), but then I stopped there. I should have kept going as it can be factored more. I could have factored the 16, resulting in 5(4x^2-1)(4x^2+1)
In the future I shouldn’t stop after one step and make sure I am completely done before finishing the question.
