Analyzing the Graph of Sine and Cosine

We have now graphed both Sine and Cosine using the pasta to illustrate the shape of the graphs. 

Review the following animation from Desmos to further clarify how we achieved this.

https://www.desmos.com/calculator/cpb0oammx7

Helpful Hints:

- To view the sine graph, click the open circle next to "Sine Animation"

- To view the cosine graph, be sure to have unchecked the sine graph and click the open circle next to "Cosine Animation"

Refer to the "Questions to Answer" portion at the bottom of the blog and answer questions 1, 2 and 3 on a separate piece of paper.

Access a second animation of Desmos by the following link:

https://www.desmos.com/calculator/nqfu5lxaij

Refer to the "Questions to Answer" portion at the bottom of the blog and answer question 4.

Questions to Answer:

Bring your answers with you to class tomorrow on a separate piece of paper

1) List at least 5 similarities between the graphs of sine and cosine.

2) List at least 5 differences between the graphs of sine and cosine.

3) Discuss the derivation of the graphs of sine and cosine, and why they are similar in shape?

4) Sine and Cosine are Trigonometric Functions, which means they are from the study of triangles, specifically right triangles. How does this information (right triangles) help us explain the horizontal (left and right) shift between the two graphs?

THE AVENGERS (2012)

The Avengers is essentially one movie but four sequels for the films: Thor, Captain America, The Incredible Hulk, and Iron Man 2.

            The Avengers starts off with Loki encountering the Other, leader of the Chitauris, who offers him an army to raid earth for obtaining the Tesseract. The Tesseract is a cube with infinite self-sustaining pure energy (which is held by S.H.I.E.L.D.). As Loki uses the Tesseract on Earth to teleport, it creates the levels of energy to spike, forcing Nick Fury (director of S.H.I.E.L.D.) to call for an evacuation. Loki uses his scepter to escape and enslave a few people, most prominently Hawk Eye. In response to Loki, Fury reactivated the “Avengers Initiative” although it was disbanded and considered untested. The initiative begins with Agent Romanoff (Black Widow) to visit Dr. Bruce Banner (The Hulk) for his assistance in locating the Tesseract due to its emission of gamma radiation. Agent Phil Coulson (of S.H.I.E.L.D.) recruits Tony Stark (Iron Man) by letting him review the Tesseract research. Fury then goes and recruits Steve Rogers (Captain America) asking him to retrieve the Tesseract.

While Loki’s minions attempt to steal iridium, he shows up in France to distract the Avengers. However this leads to Loki’s surrender and placement into S.H.I.E.L.D.’s custody. While being escorted, Thor comes and frees Loki pleading him to come back to Asgard. Thor then decided to bring Loki to S.H.I.E.L.D.’s Helicopter in which Loki is imprisoned. Banner and Stark start to locate the Tesseract. The Avengers become divided after learning S.H.I.E.L.D.’s intentions of the Tesseract, and Loki brakes out of prison. This leads to Hawk Eye losing his mind control state. Loki kills Agent Coulson in the process of braking out, forcing the Avengers to come together. Loki builds the Tesseract portal in NYC, on top of Stark’s tower. After fighting some Chitauri, the Hulk knocks Loki unconscious and takes his scepter giving it to Romanoff who closes the portal just as Iron Man forces a nuke launched by the government to end the Chitauri’s attack, through the portal. Iron Man falls through a tiny hole as the portal closes and the Avengers disband on good terms.

            For a 143 minute long movie, it doesn’t feel that lengthy at all (although it created a long summary above!). The movie flies by no matter the ’nth time watching and for an action movie, the film has several hilarious moments. The length of some action shots scenes creates a smooth fight rather than a constant cutted action scene. Applause and praise always goes to Robert Downey Jr. for his portrayal of Tony Stark / Iron Man as well as Samuel L. Jackson as Nick Fury. Mark Ruffalo, as Bruce Banner also was praise worthy with a cool and calm presence when on camera. With a storyline that doesn’t bore, interest is never lost in the movie. The visual effects are also very stellar, particularly the Tesseract portal and the Chitauri minions. Joss Whedon undoubtedly deserves recognition for a beautifully directed film. To cap off this lengthy review, I would easily give it five out of five stars.

JAWS (1975)

‘Jaws’ begins with a girl leaving a party at the beach on New England’s Amity Island. With a boy, they travel to an area of the beach where they proceed to go skinny-dipping. While in the water the girl is dragged down into the water from something below. With the coroner examining the remains that washed ashore and identifying it as a shark attack, the chief of police Mark Brody decides to close the beaches. The Mayor disagrees with Brody and keeps the beaches open to not scare away tourists. The shark kills a young boy and the mother places a bounty for the shark. This ignites an amateur shark hunting competition; in which some fisherman catch a tiger shark. Brody and a marine biologist, named Hooper, secretly open the sharks stomach to find no human remains. More tourists arrive for the Fourth of July and a man is killed again by the shark, allowing Brody to persuade Vaughan to hire Quint (who offered to kill the shark initially for ten grand), to hunt the shark down. Brody and Hooper join Quint. Eventually, they find the shark, but the shark is so large and powerful the normal techniques don’t work. The shark damages the boat to where it cannot move and starts to sink.  Having scuba gear on the boat, Brody jams in the shark’s mouth a tank of oxygen. Brody takes Quint’s rifle and fires upon the tank blowing up the shark.

            Notorious for the shark not working, this created a lack of an actual visual on the shark for most of the movie. Although this occurrence has led to many say it is brilliant in suspension. Personally I didn’t feel suspense at all while watching this film, but that could be from two factors; one being I’ve heard of the film and two I knew what eventually happens. The only shot that stands out in my mind is where they truck forward while zooming out to create a trippy background effect. Otherwise, I would say the film is shot fine. On an unrelated note, the film runs 124 minutes and that I feel is too long. Lastly, most of the scene involving Brody, Quint and Hooper talking in the cabin be done without.

            Lastly, this is what really made Spielberg – Spielberg. The shark not working worked to his advantage, and for going way over budget it certainly made the money back through the box office. All in all, the direction of this movie I would say is slightly about decent. As a consequence of its drawn out storyline and a lack of suspense to me leaves me to give the film four out of five stars.

500 Days of Summer Review (2009)

WARNING: THIS REVIEW CONTAINS SPOILERS

In 500 Days of Summer, Tom is a man who believes in some sort of destiny while Summer is a girl who doesn't share that belief. They meet at Tom and Summer's office, a greeting card company. Through initial small talk meetings and common interest they become a pair. However, they eventually break up and about one thirds of the movie revolves around their reconciliation with what occurred between the two. The film also uses nonlinear format by jumping from various days within the 500-day span of Tom and Summer's relationship. In the end, Tom gets himself back to his roots and starts looking to become an architect, ending with him meeting a new girl - Autumn.

Joseph Gordon-Levitt and Zooey Deschanel both do an outstanding job performing their character's personality and quirks. Joseph Gordon-Levitt truly makes an emotional connection with the audience whatever his mood, especially when Tom is depressed. Zooey Deschanel also captures Summer’s personality of carefree attitude and opposing views with a smooth style and powerful, meaningful dialogue. 500 Days of Summer, critically acclaimed by critics, is high on my list of favorable movies. The flow of the movie is just right, and creates almost a real effect of time and people, despite the non-linear editing. The ending is purely genius in my opinion, with a light-hearted but effective way to demonstrate how life goes on. The use of non-linear editing also entrances you to fill in the blanks in Tom and Summer's relationship.

This film is worthy of its critical acclaim position and creates an emotional interest in these two peoples lives that were nothing more than teachers for one another. On a five star rating system, the movie easily earns five out of five.

Children of Men (2006) Review

In Children of Men, Clive Owen plays civil servant Theo Faron who finds himself believing in existence and its preservation again after the world's society is approaching extinction. Children of Men's dystopian premise intuitively makes you hooked through its themes of hope, redemption and faith. Thus, the idea of infertile human beings truly resonates an alarming concept. Building off the films incredible theme, direction in the film was close to perfection with some incredible one-shots, such as the insanely chaotic car ambush scene. I would give this film four and a half out of 5 stars.

The Princess Bride Review (1987)

The Princess Bride has an elegant quirk about it that makes it slightly more entertaining than traditional romantic comedies. Though in regards to being a cult classic, I don't have much to say about it. It had no real comedic appeal nor a romantic one in my opinion. The only scene I found worth a dime was with Miracle Max. The rest of the film was predictable and drawn out aspects (such as the sword fight between Westley and Patinkin atop the cliff). Although Cary Elwes I applaud for his ability to inhibit a character that was at first extremely sweet and gentle and then instantly a tongue-and-cheek motivated swordsman/pirate. Going into technical aspects, the film was shot very oddly in my opinion. It lacked lust in it's shots specifically the sword fighting and battles in general.

The use of wide shots was overused, and some parts of the script didn't make much sense. This includes the scene where Westley is fighting off a giant rodent and doesn't have his sword and Buttercup makes no move but to stand and watch. I give this movie a half star out of five, just because it's fantasy aspects were somewhat decent (mostly the fire geysers).

Django Unchained Review (2012)

Django Unchained delivers a comedic western while containing true aspects of America's ugly past. The films comedic approach can be considered disrespectful at times, but gives the film an additional dimension that almost increases its reality of the era. The style of direction taken to this movie was praise worthy, but lacked that Tarantino flair. Tarantino's cameo was one to question too; using a weird accent, this cameo and scene had no major impact on the plot while just adding minutes to the films long running time. The acting done by Jamie Foxx, Leonardo, Waltz, and Washington was undeniably nothing short of great. However Samuel L. Jackson's character seemed a bit fake in his moral intentions. Jamie Foxx's portrayal of Django as a robust heroic badass in the distateful past of America gives the viewer a somewhat false impression of African Americans in this time. Leonardo DiCaprio's Calvin Candie creates a real depiction of a plantation owner whose morals and respect towards African Americans is nothing above a grain of dirt. This depiction creates a small window that allows the viewer to get fully involved into the story and alignment towards Django's eventual conquest. The dialogue had a very historical sense between its excessive usage of the n-word, or the conversations between white people and black people. All in all, the film is a chic, sensible film that was done near impeccably, giving it five out of five stars.