This week we learned about the sine law. The sine law was hard to understand at first but after practice it has gotten a little bit better.

The sine law can be used when you dont have very many sides or angles and can be used to find the missing sides. One thing that you must remember is it doesn’t work if there isn’t an angle and a side opposite each other.

a/sinA = b/sinB = c/sinC -to find a side length

sinA/a = sinB/b = sinC/c- to find a angle

One of the hardest parts is typing it all into your calculator properly because one small mistake of not using a bracket can totally change your answer.

We also learned about cosine and when to use that. You use it when the isn’t a angle and side opposite each other.

a^2=b^2 + c^2 -2bc cosA – side length.

cos A = b^2 + c^2 – a^2 / 2bc – Angle

Cosine law is much more difficult to use. if I can I always use sine law and if I cant I just do cosine law until I get enough information to use sine law.

In week 15 we started lesson 7.4 on adding and subtraction binomial and trinomial denominators. we also did 7.5 and 7.6.

I learned is lesson 7.4 that you can multiply each fraction by a common denominator.

To  get the fractions together you have to multiply each fraction by the other fractions denominator. once that is done it is easy to get a new equation that is better to work with.

When you have changed it you then multiply each fraction out and on there side of the equation.

We also learned the if there are only 2 fractions and there Is a equal sign between them you can cross multiply instead of changing the denominators.

In week 14 we started unit 7. 7.1 was on equivalent rational expressions, 72 was on multiplying and dividing rational expressions and 7.3 was adding and subtracting  rational expressions.

Something that I learned was you can cancel out by dividing number from the numerator and denominator before you multiply or divide. and you are not able to cancel out numbers if it is addition or subtraction.

If you have a expression 36/3 * 18/6  you can simplify them.

36 and 6= 6/1

3 and 18= 1/6

Doing that makes the expression much easier to work with.

In week 13 we continued to learn about chapter 8. we did lessons 8.2, 8.3, and 8.5.

In lesson 8.2 we learned about absolute value equations.

In lesson 8.3 we learned graphing reciprocals of linear functions.

In lesson 8.5 we learned graphing reciprocals of quadratics.

It is really fascinating to see how the reciprocals look in a graph because they all look very different from each other. there were also different numbers of parent functions the a parabola has affects the shape of the hyperbola. 0 root, 1 root and 2 roots all have different graph shape.

It was also cool to learn the in the hyperbola will never cross along the X axis.

In week 12 we learned lesson 5.5 and reviewed for our test.

One thing that I learned is how to put a quadratic equation and linear equation and put  them together to find the root (x) and replace in the original equation to find (y)

Example

y = 3x + 7 and
y = X2 + 4x +3

X2+4x +3 = 3x +7

Then you move it all to either side but you should try to keep the X squared (X2) positive.

X2 -3x -4

Now you can just factor and solve for X

For week 11 of pre calc 11 we continued learning about unit 5, graphing systems and inequalities, lesson 5.2,  5.3,  5.4.

I learned about having different  lines on your graph due to the different symbols that are in your equation. If the symbol is  <  then the line is the graph is dotted. If the symbol is ≥ then the line in the graph is solid.

we also learned about solving systems graphical and we learned how many solutions each system could have. parabolas can have 0,1,2, or infinite.

In week 10 we were studying for the midterm. I studied unit 3 and a little of 4 because I did not do so well on those sections before.

Unit 3 was quadratic equations. The different ways to solve one is by factoring, quadratic formula and completing the square.

One thing that I did struggle with while studying was the word problems that made you put numbers into a quadratic equation.

A example of a word problem is: Two different numbers have a maximum product and a sum of 6.

a + b =6

a x b = maximum

b= 6 – a

a x (6-a) = product

6a – a(sqr)

In Week 9 we did lessons 4

4.5 and 4.6 focused on the 3 formulas: General, Standard and Factored Form. in the lessons it taught us how to convert one form to another to find out different parts to the parabola.

Example: General-Factored

Week 8 we began reviewing for the mid term and started lesson 4.

In lesson 4.1 we learned about new concepts like the vertex. A vertex is the highest or lowest point on the parabola graph.  Other vocabulary we learned were:

• Vertex: Lowest/highest possible point
• Congruent graphs: if the graph has the same shape as the parent function (y = X2)
• The x-intercepts: the point were the line passes through the x-axis
• The y-intercepts: the point were the line passes through the y-axis
• Direction of opening: Whether the graph opens down or up               ( minimum-up) (Maximum-down)
• Axis of symmetry: the point that splits the graph down vertically

We also used the table of values for looking at outputs of Y values.

In lesson 4.4 we learned 3 different equations.

For week 7 we had the final lesson in unit 3 and then had a unit test.

In the lesson we learned a new simple concept or equation b^2-4ac

This formula determines if the equation is even solvable or not and ow many roots it will have.

We can then completely solve the formula if the product is bigger than 0. If the product id bigger then 0 it will have either 2-1 roots and if it is equal to 0 it will have 1 root.