Using reference angles to find the six trigonometric function values
Lesson Outline
I demonstrated for Olivia how the coordinates of the terminal point can be used to calculate the radius using the distance formula. I then showed her how to calculate the six trigonometric functions using the definitions in terms of x, y, or r, the radius. We began doing more problems at the end of the session. There was no assignment.
Assignment
See lesson outline
Session Minutes
60
Minutes Student Attended
30
Lesson Comments
Olivia was 17 minutes late starting the class and then excused herself to use the 'rest room' for another nineteen minutes. I have therefor awarded her only 30 minutes of attendance.
Per my other session note, as Olivia was 35 minutes late to English and then took a prolonged restroom break, I extended the English class a few minutes instead of conducting 10-15 minute Government class.
As Olivia's essay on "Their Eyes Were Watching God" was quite impressive, we spent most of today's session highlighting the essay's insightful analysis as well as discussing ways to increase the force of the essay by polishing some sentences and addressing some word usage. We broke one of the longer paragraphs into three separate paragraphs, rewrote sentences where the pronouns did not clearly relate to any antecedent , and addressed spelling errors. As the essay required a comparison between the theme of the novel and the theme of two poems, we discussed ways to rewrite the transition paragraph followed by rewording some of the analysis with more vigorous verbs instead of "is ,were" or other forms of the verb"to be". We further worked a few more lines from the poetry into the essay. Last, we addressed the construction of the last sentences so as to eliminate the word"you" which is not preferred in formal English. Olivia proved to be a good editor of her own words. The essay was excellent . We then reviewed Hemingway's introduction to the novel " A Farewell. to Arms" noting his anti -war rhetoric. With that background , Olivia examined the text to locate the anti-war sentiments and aptly commented on the unemotional style of the the diction when the author describes the death of soldiers. As is often necessary in reading Hemingway, we discussed the absence of narrative and discussed the implied narrative lurking beneath the text. For homework I assigned reading through. ch 18 .
Session Minutes
75
Minutes Student Attended
75
Lesson Comments
As Olivia missed the first. 30 -35 minutes of English class and then took a prolonged restroom break, I extended the English class a few minutes .As a result, we did not have a government class today.
Using reference angles to find trigonometric functions
Lesson Outline
I worked with Olivia to explain several examples of using reference angles to find the trigonometric values of angles larger than 90 degrees. I demonstrated how the values are symmetric around the unit circle with signs appropriate for the various quadrants. We also explored angles larger than 360 degrees. There was no assignment.
Assignment
See lesson outline
Session Minutes
60
Minutes Student Attended
30
Lesson Comments
Olivia did not start the class until 15 minutes into the session. After about 20 minutes, she asked to use the 'rest room'. I said yes and Olivia took about 15 more minutes out of class. I have decided that she missed at least half the class, and therefore, she got credit for 30 munutes of class time. She was also not well focused.
During most of the session ,Olivia took a test on the Federal Court System. She scored an "A " on the test . During the final minutes of the session, we continued our study of the First Amendment focusing on the right to petition the government. I explained the scope and reach of the right to petition including how ballot initiatives are manifestations of that right. We commented on how ballot initiatives grant citizens the right to bypass the legislature when the legislature fails to act in accord with the will of the voters. For homework, I assigned reading pages 450-452 and answering one study guide question.
Olivia has prepared two written assignments analyzing "Their Eyes Were Watching God" which we reviewed today. With respect to the interpretation of quotes from the novel, we addressed eliminating duplicative ideas and combining sentences. We further discussed techniques to convert the prompt into a topic sentence and the need to keep the focus of the essay on the prompt's inquiry. We next reviewed the meaning of the metaphors contained in the quotes. Olivia 's most recent essay was excellent. I did ,nevertheless , provide some instruction on creating a transition sentence to segue into her discussion of the poetry and addressed some grammatical concerns with respect to run-ons. As such, during the last part of the class, Olivia completed some grammar exercises on run-ons and fragments which we will continue tomorrow. She did very well with the exercises. For homework, I assigned reading ch 10 of
Farewell to Arms".
I showed Olivia a few more solutions for missing sides of right triangles. We then started the next topic, Trigonometric functions of any angle. I demonstrated how any angle can be drawn as a line segment from the origin with a set radius of 1 and an x and y coordinate at that distance. We then reviewed the definitions of all the trigonometric functions based on the values of x, y, and r. There was no assignment.
Assignment
See lesson outline
Session Minutes
60
Minutes Student Attended
60
Lesson Comments
Olivia was very distracted as I was working with her. It didn't seem like she was paying attention.
The First Amendment prohibits prior restraint of the press. But what if national security is at risk? Olivia discussed prior restraint in this context and discussed the case of US V.New York Times wherein the US Supreme Court refused Nixon's request to prohibit the Times from publishing the Pentagon Papers. We examined various scenarios where failure to prohibit the press from publishing classified information could place citizens at risk and the tenuous balance that exists between informing the citizenry and upholding the First Amendment. In that regard, we discussed Julian Assange and Wikileaks and examined both sides of the debate as to whether Assange is a patriot or a traitor. Examining a similar difficult balance, we then studied the right of the press to cover a sensational trial when the coverage compromises a criminal defendant 's right to to fair trial.I discussed the Sam Sheppard case and F. Lee Bailey's role in overturning a conviction due to the circus atmosphere created by the media. We then discussed jury sequestration and whether in the age of smart phones sequestration remains effective . Tomorrow ,we will be having a test on the federal court system.
We studied the hidden narrative in Hemingway's style by analyzing the ongoing dialogue between Lt. Henry and Catherine. Olivia offered a strong analysis of the exchange as a "skit" wherein the two characters vocalize words of love they both know are not true but need to be true given the fragility of their lives in war. I then read two passages that highlight Hemingway's journalistic terse style, and again we searched for the 7/8 of the iceberg below the surface meaning of the sentences themselves. Last, we located portions of the text foreshadowing that the characters are undergoing some type of character development . In that regard, Olivia discussed how the first person narrative informs the reader that the story occurred in the past in that the reader is told the characters do not know early on what they will later learn. But ,of course, Hemingway does not yet explicitly tell the reader what it is the characters later learned .Olivia then offered speculation about themes the novel will develop and what the major characters may learn from their wartime experience. For homework, I assigned reading the next two chapters.
Olivia and I continued to find trigonometric functions of various angles. We also used trigonometric identities to transform expressions into ones we could use to find required values. We finished the lesson solving for the sides of triangles from given angles and other sides. There was no assignment.