## Precalc 11 – “Week 17”

This week in Precalculus 11 we learned about trigonometry. During the week we improved our understandings of trig and learned two new laws for trigonometry.

The first law is the Sine Law:

$\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}$

The Sine law is used for triangles with no angle being 90 degrees. It can only be used when A, a and either another side or another angle; A, B and c.

The second law is the Cosine Law:

$a^{2}=b^{2}+c^{2}-2bcCosA$

The Cosine Law can only be used for triangles that have the three sides or when a,c and B are known.

Thank You for Reading!

## DOAS Monologues

I am a mother of two grown sons. I believe my sons are not doing much with their lives and with that, they cannot criticize my husband for daydreaming occasionally. I am an old woman with grey and white hair, as a stay at home mother and wife. I am very mellow, because I try to be the best wife I can be to my husband, Willy. I know more than other believe I do, as I am very good in math, better than my husband is in math. I also have known for the last few weeks that my husband has being trying to asphyxiate himself with gas using a plastic pipe attached to the radiator, however I am too scared to remove it, with the possibility that it would humiliate him. I am very loyal to my husband and I believe he can do no wrong, and I am more loyal to him than either one of my sons. My husband lies to me about his financial earnings, and I act as if I did not know, because I am worried that it will push him to the edge and he will suicide. That is why I am very timid and anxious towards my husband. I spend most my days worrying about him, wondering if he will get in another car accident.

## Blackout Poem – “I Know Why The Caged Bird Sings”

The poem, I Know why the Caged Bird Sings, by Maya Angelou can be interpreted as a poem about freedom of the oppressed people. The speaker talks of two birds: one free and one caged. One bird can roam through the sky as he wishes, taking any route, whereas the other bird is caged “his feet are tied”, “his wings are clipped” and “The caged bird sings”, this bird cannot do as he wishes, and all he can do is sing, (Angelou 12-13). The connotative manner to interpret these stanzas is that the bird, whom can fly anywhere he wishes, is Caucasian people in the US of A, whereas the caged bird is the African Americans of the US of A, whom can only talk to express their oppression. The thematic statement apparent throughout the poem is that even if one cannot moved, no one can oppress your voice or your opinion, “The caged bird sings/ with a fearful trill/ of things unknown” and “his wings are clipped and/ his feet are tied/ so he opens his throat to sing” (Angelou 15-17, 12-14). These two quotes represent the thematic statement, because they are stripped of all their physical rights, but there are no ways to take away someone’s opinion. Repetition or refrain can be seen in the poem to emphasize the multitude of the situation that African Americans feel. There is also various moments where we can see personification, “his shadow shouts” (Angelou 28). Maya Angelou uses a lot of imagery throughout the poem, “free bird” and “caged bird”, are the two most obvious uses of imagery, each signifying people with no restrictions and people with restrictions. I Know why the Caged Bird Sings, by Maya Angelou is very informative on how oppressed African Americans felt towards the way they were treated before they had the same rights as everyone else.

## Precalc 11 – “Week 15”

This week in Precalculus 11, we learned about multiplying, dividing, adding and subtracting Rational Expressions. The hardest part about this unit was simplying rational expressions which had adding and subtracting, especially if these were the denominators:

$\frac{4}{x-5}+\frac{x-7}{5-x}$

Because $x-5=-1(5-x)$, Therefore

$\frac{4}{x-5}+\frac{-x+7}{x-5}$

$\frac{4-x+7}{x-5}$

$\frac{11-x}{x-5}$

Thank You for Reading!

## Precalc 11 – “Week 14”

This week in Precalculus 11, we learned about graphing reciprocal functions. The hardest part about this was graphing quadratic reciprocal functions, because there are three different forms depending on how many roots it has.

Here are the three different ways:

1.Contains one roots:

$y=\frac{1}{x^2+6x+9}$

2.Contains two root:

$y=\frac{1}{x^2+6x-9}$

3.Contains zero roots:

$y=\frac{1}{-x^2+10x-30}$

Thank You for Reading!

## Precalc 11 – “Week 13”

This week in Precalculus 11 we learned about Absolute Value Functions. We have already done absolute values which is:

$\mid-3x+5\mid=11$

Which is $3x=6$

$x=2$

Absolute values turn the equation positive. Therefore an Absolute Value Function can only be positive.

$y=\mid-3x+5\mid$

As you can see the blue line is $y=-3x+5$, and because absolute values need to be positive then the line cannot be below the x-axis, therefore it is flipped as you can see by the red line: $y=\mid-3x+5\mid$

Thank You for Reading!

## Precalc 11 – “Week 12”

This week in Precalculus 11 we learned about how to solve quadratic systems.

Most questions were based on two lines either quadratic-quadratic or linear-quadratic.

There are multiple ways of find the solution for where both lines cross, like graphing or elimination. However in class we learned about the process of substitution.

Which is removing one variable from the equation and then solving for the remaining unknown variable. After that using that answer to find the first unknown variable.

ex.

$y=2x+5$

$y=x^{2}+6x+9$

$2x+5=x^{2}+6x+9$

$0=x^{2}+4x+4$

$x=2$

$y=9$

Thank You for reading!

## Precalc 11 – “Week 11”

This week in precalculus 11, we learned about graphing linear inequalities.

This is what we learn:

If the inequality was greater than or equal to y:

$y=<2x+2$, then you also need to shade the line.

Same goes for an inequality which is less than or equal to y.

However if it is only greater than or only lower than, then you must leave a dotted line to inform that the line does not count as part of the answer.

Thank you for reading!