### Archive of ‘Math 11’ category

This week in Precalc 11 I learned the Sine law. The golden rule when it comes to Sine law is ” You can only use this law if you have at least one angle and its corresponding angle”, if you don’t have an angle and its corresponding side then you can not use this law.The formula for the Sine law also differs whether you are finding an angle or a side. Today I will be going through how to use Sine law when you are finding a side.

If you are finding a side, the formula is :

If you are finding an angle then you just flip it:

Here is an example and the steps I would take when solving for a side using the Sine law:

This week in precalculas 11 we learned about special triangles. We use these special triangles when the angle is 30, 60, and 45 degrees. For these special triangles we will not have to use a triangle and they give us a more exact answer.

These are our special triangles:

This is an example and the steps I would take to solve for an angle:

A question I struggled with this week was:

I was doing alright until I was at the solving step:

As you can tell, I was conflicted about whether I should cancel the two out or not, and the answer is yes because they are opposites.The rule says you can but you have to put a negative one (-1) in the numerator.

This week in Precalculas I learned how to identify the Non- permissible values of a rational expression. A non – permissible value is a number that would cause the denominator to equal zero. An example on how to find one while simplifying or solving an expression is this:

This week in Precalculas 11  I learned how to graph an inequality. The main difference between inequalities and equations is that equations are equal to 0 and inequalities are not. An inequality can come in many forms and symbols that show the inequality. For example, there is the Greater than symbol >, Less than symbol <, Greater than or equal to symbol ≥, and the Less than or equal to symbol ≤. The symbols determine which part of the graph the answer will be on. If the symbol is equal to and has a line below then it means the point on the graph will be a filled in circle. If it is not equal to then it doesn’t include the point and the circle is not filled in. The other thing we learned this week is how to write answers in interval notation. This is where you use different brackets and symbols to determine what the answer is. For example, if you consider the fact that the lines don’t have domains or ranges and they go on forever if they don’t have a point it would be infinity  (∞), this is only if it’s moving to the right of the number line and is greater than 0. If the lines go on forever but are moving to the left of the number line and is less than 0, then it will be a negative infinity sign ( – ∞). Also when you write in interval notation if the number has a filled in circle and it is equal to then you would use a square bracket, [, ]. If the number is a non – filled circle and is not equal to, you would use round brackets (, ). We also use the round brackets when you are describing the line or parabola with ∞. An example of writing something in interval notation would be (-∞, 5]. Another key note is that if the x is on the smaller end of the symbol x<0 the area that we are focusing on is the inside part of the parabola. If it is the opposite and x>0 then the part we focus on is the outside of the parabola. Another important note is that whenever you are solving an inequality you must always flip the symbol when you divide by a negative.

This week we mostly did review because we have a midterm coming up. While I was looking through the practice test I noticed a question from one of our earlier units and I didn’t get it right first try. Then I realized that I had to use exponent laws:

At the beginning of this week in pre calc 11 we learned about Vertex/Standard form. This is personally my favourite form because it provides more information about us graphing the quadratic function than the quadratic or factored forms give us.

Vertex/Standard form looks like this:

$y=a(x-p)^2+q$

This form provides you with the following information about a parabola:

a:

1- tells us whether a parabola is opening up or down. If it’s a positive # than it’s opening up, and if it’s a negative # than it’s opening down or being “reflected”.

2- determines the size of our parabola, whether it is stretched or compressed. If a is greater than one then the parabola is stretched, if a is less than one then the parabola is compressed.

p:

1- tells us the horizontal translation of a parabola (whether the vertex is moving left or right).

2 – tells us what our line of symmetry is.

q:

1- tells us the vertical translation of a parabola (whether the vertex is moving up or down).

p & q:

1- the p and q are very important becuase they let us know our vertex *the vertex is the most important part of any parabola. The p tells us our x co-ordinate and the q tells us our y co-ordinate for when we are graphing a quadratic function.

This week in pre calc 11 we started chapter 4, and the first thing we learned was properties of quadratic functions. Now it’s important that before we start listing off the properties of each of these quadratic functions, that we know 100% that this is a quadratic equation. How can we tell if a function is linear, quadratic, or neither. In this blogpost I’m going to show you how you can tell the difference between a quadratic function and a linear function by looking at the table of values for any type of function.

Linear – look at the first differences, if they are equal to each other than it is a linear function.

Quadratic – Look at the second differences, if they are equal to each other than it is a quadratic function.

Neither – Than it just simply doesn’t follow any of the rules from above and is not a linear or quadratic function.

Ok so lets begin, suppose we have this table given to us:

The first step is to find the first difference, how you do this is to find how much space is between each of the #s.

As you can see, the first differences are equal to each other therefor this is a linear function.

Let’s look at another example:

Follow the same steps as you did for the function above:

As you can see, the first differences aren’t equal to each other so now we have to find the second differences:

The second differences are equal! Therefor this is a quadratic function.

Lets look at one last example:

First – find the first differences:

The first differences aren’t equal so we move on to step 2 – finding the second differences:

For this example both the first and second differences are not equal therefor this is neither a quadratic or linear function.

This week in pre – calc 11 we learned chapter 2.6 – solving equations algebraically. One thing that stood out to me was learning how to rationalize the denominator to solve an equation that looks like this one:

The first step is to multiply the $\sqrt{3}$ “rationalize” it. The $\sqrt{3}$ multiplies with everything and cancels out the $\sqrt{3}$ on the bottom of the equation.

The next step would be to further simplify but as we can see we no longer can simply this equation further, so we leave it like this

Here is an example of an equation which also requires to be rationialized, take a couple seconds and try to solve this using what you know about rationalization:

Below is the answer and me solving this equation using rationalization: