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This week in Precalc 11 we learned a new trigonometry formula known as the sine law. Sine law is used to find the angles and side length of triangles that don’t contain a ninety degree angle. To use this formula you need 3 pieces of information, 2 of which must correspond to one another. For example if you have angle C you need the side length c.
The equation you can use for sine law is:
The equation for sine law can be reciprocated depending on what you are trying to find. If you are looking for an angle, you would put the sin’s in the numerator and the side length in the denominator. Vise-versa with finding a side length.
When solving with sine law, you must choose on fraction that has a completed numerator and denominator and another fraction that has either the numerator filled out or the denominator.
Then you must isolate the variable. To do this you have to get rid of the uncompleted fractions denominator and you also must get rid of the trig function attached to the variable on the numerator. To do this you must take sin and inverse it. For example:
Two things I did well:
1. Sensory detail and descriptivity
2. Creating a story that accurately represents everything I wanted it to
Two things I can improve on:
1. Quote intergration
2. Reading over carefully to catch little mistakes
Sticks and Stones
Contrary to popular nursery rhymes and sayings, words leave marks as deep and painful as sticks and stones. A word with no more than one syllable can silence a room and exasperate a culture using less than a breathe. If these words cause so much harm then why would we use them? Teams such as The Cleveland Indians, Chicago Blackhawks, Washington Redskins, and Edmonton Eskimos are all examples of taking words commonly used to appropriate a culture, and turning them into entertainment. Words such as Redskin stem all the way back to 1769; not only was it used as a derogatory term, it was used to describe the torturous scalping and skinning opposed onto the First Nation. Today the word is used to describe a football team which has won three Super Bowls; this team is depicted by a drawing of an Indian chief wearing a head dress with feathers, and cheerleaders who wear long black braids. Not only is the word connected to a dark past, they are portraying the Native Americans stereotypically. Many Aboriginals, including, Susan Harjo have filed a petition against the Patent and Trademark Office asking for the revocation of the team’s six federal trademark registrations, because of the disparagement upon the community. However, with the many people petitioning the court no change was made until 2014. With this being said, studies show that seventy-three percent of Native Americans were not bothered with the word, “redskins,” and only twenty-six percent were bothered by the use of Native American imagery in sports. Furthermore, the aboriginals have no doubt been through hardship, but it is not over for them; the issue of sports teams seems rudimentary to the trouble which faces their reserves. Most people wouldn’t think about the burdens they face; in their minds Natives live off the land with buffalo skins and spears. These perceptions, these stereotypes, drive from the medias notion of their culture. They see The Cleveland Indians, Chicago Blackhawks, Washington Redskins, and Edmonton Eskimos versions plastered on their uniforms, merchandise, and billboards, but they don’t see the truth. They don’t see who chief Blackhawk really was, and what war he fought in. They don’t know that Eskimos are really known as Inuits and that just because they don’t look like Pocahontas doesn’t mean they’re not indigenous. As Winona Linn once said in a spoken word: “ He could only call me out because of the colour of my skin but my skin doesn’t match his perception of Indian,” ( Linn, 2013) because they only see the transparent mask put upon their culture. If you were to replace the derogatory terms or crude cartoons with any other culture, light would shine upon the immorality. Light would shine on the sticks and stones.
Shapira , Ian. “A brief history of the word ‘redskin’ and how it became a source of controversy.” The Washington Post, WP Company, 19 May 2016, www.washingtonpost.com/local/a-brief-history-of-the-word-redskin-and-how-it-became-a-source-of-controversy/2016/05/19/062cd618-187f-11e6-9e16-2e5a123aac62_story.html?utm_term=.29f3f591d492.
“Poll: Native Americans’ attitudes toward the Washington Redskins team name.” The Washington Post, WP Company, 19 May 2016, www.washingtonpost.com/apps/g/page/mobile/sports/poll-native-americans-attitudes-toward-the-washington-redskins-team-name/2034/.
PoetrySlamVancouver, and Winona Linn. “ Knock-Off Native.” YouTube, YouTube, 30 Jan. 2013, www.youtube.com/watch?v=i_zFOsd_pqA.
This week in Precalc 11 we learned how to multiply and divide rational expressions. The General rule for doing this is:
1. Factor (numerator and denominator)
2. Use exponent laws
3. Cancel out like terms
this process is much like cross multiplying, for example:
since these fractions can get pretty long and “ugly”, writing them out is helpful and easier to manage. If you follow the 3 main rules as well than solving is much more efficient.
Monomials are easier because you can combine the numerators and denominators than simplify.
When it is a single variable expression you must factor in order to simplify. You can only cancel out EXACT terms. The + or – signs act as unpenatratable glue. They connect the numbers on either side of the sign, acting as a package.
To cancel out you can use the cross multiplication technique. Then combine the leftover numerators and denominators.
The last thing you must do, which you actually do first, is find the non-permissible values. A non-permissible value is the numbers which make the denominators equal to zero. You find these once you have factored.
This week in Precalc 11 we learned about equivalent rational expression. Rational numbers are quotients of two integers. So, two polynomiales are known as rational expressions. E.g:
to simplify a rational expression the first thing you must do is find the non-permissible values. A non-permissible value is a number which makes the denominator zero because, you can not have a fraction with a zero as the denominator.
To find this value you must find the zeros meaning figure out what numbers would create the equation to become zero. You can do this by inspection or factoring.
After you you have figured out the non-permissible values you can then cancel out common factors. These factors must be the exact same in order to cancel out.
this week in Precalc we learned how to solve linear absolute value equations algebraically. the first step in doing this is split the equation into two different equation. One of the equations being the same as the original but without the absolute brackets. The other equation is too the same without absolute brackets, but has a negative sign in front. For example:
from there you solve the linear equations the same way you solve any other linear equation.
Once you’ve figured out X you must verify it to check for extraneous roots. To do this you can just plug the X value back into the equation. If the right side balances out with the left than it is not extraneous, but if it doesn’t than the root is in fact extraneous. Another thing you can do that will save you time is take the absolute value and create a restriction. From there you compare it with your Answer. If the statement is true then you do not have an extraneous route.
To determine what inequality to use think about what equation you’re using. For the original one you want to know what numbers you can use from the zero which will result in a positive. Same thing for the peicewise equation. You want the equation to result in a positive as well and sometimes you will need a negative
The meanjng of this movie is heavily based around “carte diem”, meaning to seize the day. Mr. Keating teaches the boys a valuable lesson about how short life is and in that little bit of time you have to make it worth it. He taught them that you do not have to conform to your teachers and parents; you are your own individual that can make your own choices and take your own paths, even if it’s the “less travelled one”. This move connects to Macbeth soliloquy tomorrow, as they both connect to the meaning of life. Keatings meanjng is much more hopeful and motivational, rather than, Macbeth who has a more dreary look on life. He believes that life is pointless. It too may be short but the time spent alive has no impact and is meaningless. He doesn’t believe that there is any point to “seizing” the day.
I think this movie was really good. It had a very important message that could still be connected today. Many people try to conform into society and that still leads people to take their lives, much like Niel. The movie was very engaging and I never once looked away. I would definitely watch this again and would for sure take the meaning of this movie with me.
this week in Precalc I learned how to graph linear inequalities that contain 2 variables. Solutions to a liberal equation with 2 variables is represented by a boundary line and shading in one side.
A solid line for an inequality:
A broken line for an inequality:
to graph it you take the line and convert it to y=mx+b form. Things to look for in this form is the: Y-intercept so you have a point to start from, the X coefficient so you know the rise over run, and the inequality sign to figure out if the boundary line will be solid or broken.
Once you’ve graphed the equation, choose a test point. You can choose any point and plug it into the x and y spot. If the equation is proven true after solving, than you shade that section. If not the equation is false and you shade the other section. The two test points I’ll use is (0,0) and (-5,5)
This week in Precalc 11 we learned how to solve a quadratic inequality with one variable using a sign Chart.
The steps when using a sign chart is to:
1. Factor expression
2. Determine zeros
3. Use a sign chart for each factor
for example, take this equation and make it equal to zero the factor.
Once you have factored determine the zeros (-3/2 and 4) and place them on two number line. Each number line will represent a different factor. One will be (2x+3) and one will be (x-4).
For each factor do a test point in all 3 sections. Pick a point less than -3/4, between -3/4 and 4, and greater than 4. Plug these test points in to the factor and determine whether the outcome is negative or positive.
Add up the positives and negative of the two number lines to determine what the equation will finally equal.
Since the equation is asking for the equation to be less than zero we want x to be negative.
Two things to improve on:
1. Writing clear thesis statements that effectively prove my point
2. My grammar
Two things I did well:
1. Having a unique writing style/ voice
2. The hook and conclusion