on I used Genially, Canva, iMovie, and YouTube to craft an interactive photo project focused on key themes introduced by Trevor in his book. Each information dot is dedicated to a distinct topic, connected to a symbol that resonates with the narrative and events depicted in the book. The original voice recording through my genially link was not working so i just attached the recording to the post.
Born A Crime – English 12 Core Compentecy
on This week i learned about Co-terminal angles and how to find them…
Co-terminal angles differ in the number of full rotations around the unit circle, but they share the same beginning and terminal sides as the provided angle.
Let’s do an example to show my understanding…
Find a positive Co-terminal angle to -45 degrees.
to find the Co-terminal of a given angle to you all you need to do is…
You add or subtract multiples of 360 degrees…
So…
Add 360 degrees to -45 degrees
-45 + 360 = 315 degrees
So, 315 degrees is a positive coterminal angle to -45 degrees.
That is all you need to do find coterminal angles!!
on This week i learned a Continuation of the last weeks lesson basically Cosine Law!!
I really enjoyed working with these laws as i didn’t find them as confusing as the other Law’s we’ve had to deal with during Pre Calculus 11 like the Power Law, etc…
First things first Cosine Law goes just like how the Sine law is but there is couple ways you can write the law so find what you are seeking for…
c² = a² + b² – 2abcos(C)
Let’s do an example to show my understanding…
Think of a triangle with side lengths of a = 3 units, b = 4 units, and an angle C between those sides, measuring 60 degrees. We want to find the length of side c.
Start with the cosine law equation
c² = a² + b² – 2abcos(C)
Plug in the values that you know of or that was given in the question
c² = 3² + 4² – 2(3)(4)cos(60°)
Use a calculator for this part as it obviously will be tough solving for a angle…
you are left with…
c² = 13
Square root both sides as you know it’s what’s needed to get rid of the exponent…
You are finally left with the exact/approximate measurement of side C..
Which is!!
c = √13 or c = 3.6055
There we go!
on This week i learned how to do the Sine Law!!!
First things first what is the Sine Law?
It consists of a equation that looks like this…
a/sin(A) = b/sin(B) = c/sin(C)
Let’s do an example to show my understanding…
Consider a triangle with side lengths of a = 4 units, b = 5 units, and an angle A opposite side a, measuring 60 degrees. We want to find the measure of angle B.
Start with the sine law equation
Plug in the known values of the question
4/sin(60°) = 5/sin(B)
Then solve for sin(B)
4 * sin(B) = 5 * sin(60°)
Cross Multiply there..
Then solve for sin(B)
sin(B) = (5 * sin(60°)) / 4
Calculate B using a calculator
B = sin^(-1)((5 * sin(60°)) / 4)
B = 43.2°
The Value of angle B is 43.2°
There we go!
on This week I learned how to turn standard form into factored form to determine the zeros for quadratic functions!
I’ll show you my understanding by converting the quadratic function f(x) = x^2 – 9 to factored form to determine it’s zeros
Notice that this quadratic is a difference of squares!! We can rewrite it as…
f(x) = (x – 3)(x + 3).
The factored form of the quadratic function is (x – 3)(x + 3)
To determine the zeros of the function, set (x – 3)(x + 3) equal to zero and solve for x!
(x – 3)(x + 3) = 0.
So the solutions that lead to zeros are x1 = 3, x2 = -3..
Equation was already in the form of difference in squares thus it was easier to work with and to find out what its zeros were.
on This week i learned how to solve rational equations! (watch out for extraneous roots)
To show my understanding lets solve the rational equation (1/x) + (1/(x + 1)) = 1/2
Find out what the common denominator is,
Multiply both sides of the equation by x(x + 1) to get rid of the fractions
x(x + 1) * [(1/x) + (1/(x + 1))] = x(x + 1) * (1/2)
By doing this it simplifies the equation down to…
(x + 1) + x = (x)(x + 1)/2
From here on out you can solve the rest by…
x + 1 + x = (x^2 + x)/2
Expanding and Simplifying
2x + 1 = (x^2 + x)/2
Multiply both sides by 2 to get rid of the denominator…
4x + 2 = x^2 + x
Then rearrange the equation
x^2 + x – 4x – 2 = 0
Combine like terms again
x^2 – 3x – 2 = 0
And you are left with a quadratic equation you can either double check your answer what the solutions are by using these certain methods that will get you your answer which can be Completing the square, Quadratic Equation, Factoring.
Factoring the equation above seems easy enough so lets do so,
(x – 2)(x + 1) = 0
so x1 = 2, x2= -1 are the solutions
If you want to be certain about your solutions you can plug either numbers in for x to make sure you get the same number on both sides, which then you’ll be certain that you were right.
on This week i learned… How to solve for non permissible values!
Lets try this equation
y = (x^2 + 3x – 4) / (x – 1)
So we are solving the x and what number does it need to lead to zero? It’s (x+1) thats the non permissible value
To double check our answer we could use the substitution method of plugging 1 in to where the x’s belong in the original equation.
y = (1^2 + 3(1) – 4) / (1 – 1)
So when solving for it you end up with…
y = 0 / 0
Therefor you are left with zero which makes the equation undefined and that 1 is truly your non permissible value for this quadratic problem/equation.
on This week i learned how to solve for inequalities!
Here is an example i could show you to explain my understanding,
4x + 3 > 11
First thing you do is to move the three over so you have to minus 3 from both sides to create a zero pair on the left and your left with,
4x > 8
Now all you have to do is divide by 4 so you isolate the x as its the whole point of solving inequalities.
x > 2
Is your final answer!
on This week I learned…
About Vertex’s, Line of Symmetry, Parabola, Maximum & Minimums, X & Y Intercepts!
Vertex is a point where two or more lines meet on the axis.
Line of Symmetry is the middle point of that Vertex. that cuts it in half exactly.
Parabola is a U shaped curve that opens up or opens down on a graph.
If the Parabola is opening up then thats where the term Minimum comes in.
If the Parabola is opening down then thats where the term Maximum comes in.
X-intercepts and Y-intercepts are points where a curve or line intersects the X-axis and Y-axis
The x-intercept is the point at which a graph crosses the x-axis. This means that the y-coordinate of the point is zero. It will always be zero for it to be considered a X-intercept same rule applies for Y-Intercepts.
y = 2x – 6
First things first is that in this question you rid of the constant number so you add 6 on both sides to move the 6 over to the left side so the question becomes,
6 = 2x
Being left with this you have to now divide both sides by 2
So now you are left with
3 = x
The X intercept is seen to be x = 3 (3,0)
on This Week I Learned…
How to solve by factoring!
This is the example i’m using to demonstrate my understanding of factoring,
x^2 + 5x + 6 = 0
First things first see if you can find any factor and possibly make the question easier as. soon as possible but the equation can’t seem to be broken down any further so we move on,
Next step is to find two numbers that multiply to the third term which is 6 and that also add up to 5
Those two numbers will be,
2 x 3 = 6 (C) (Third Term)
2 +3 = 2 (B) (Second Term)
So now we can rewrite the middle term of the quadratic expression using the two numbers we found!
x^2 + 2x + 3x + 6 = 0
Now you are able to group them,
(x^2 + 2x) + (3x + 6) = 0
You can factor them out further more as it shows on the right side as that binomial can be broken down furthermore.
x(x + 2) + 3(x + 2) = 0
You can still go down further, So keep on going.
(x + 2)(x + 3) = 0
So for the solutions are the numbers that just basically add up to zero
So the solutions are…
(x1 = -2), (x2 = -3)