Large assignment/exam trigonometry

Math 1120 Name (Print): 2020 Exam 1 Week 2–3 Time Limit: Two days Lecture Day/Time

This exam contains 11 pages (including this cover page) and 6 problems. Check to see if any pages are missing. Enter all requested information on the top of this page, and put your initials on the top of every page, in case the pages become separated.

You may use your book, former homework problems, Teams posts/discussions, or any notes from the course on this exam. You may use a graphing calculator for inspiration or guidance, but you must show every step leading to what your calc

You are required to show your work on each problem on this exam.

The exam is due by Saturday, 9AM. If you have an accommodation granting you time and half, then your exam is due Sunday, 9AM and your exam should be emailed to me directly.

The following rules apply:

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• Organize your work, in a reasonably neat and coherent way, in the space provided. Work scattered all over the page without a clear or- dering will receive very little credit.

• Mysterious or un- supported answers will not receive full credit. A correct answer, unsupported by calculations, explanation, or algebraic work will receive no credit; an incorrect answer supported by substantially correct calculations and explanations might still receive partial credit.

• If you need more space, use additional sheets of paper and insert them appropriately so that the scanned exam is one continuous PDF. In other words, do not put extra scanned sheets out of order.

• The exam is graded out of 120 points.

• Good luck!

Do not write in the table to the right.

Problem Points Score

1 20

2 20

3 20

4 20

5 20

6 20

Total: 120

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Further instructions

1. Restate the problem in its entirety if you are going to write on separate sheets of paper. If your answer spans multiple pages, then indicate ”Problem # Cont.” at the top of the next page. You may use white or yellow lined paper, solid white paper, or engineering paper. You may also write on an electronic tablet (e.g., iPad) but your work must be compiled as a single PDF.

2. Do not start a new problem on the same sheet as a previous problem. Points will be taken off if you don’t follow this rule.

3. Answer all problems in the order they are asked.

4. Write clearly, in complete sentences and make sure your scan is equally clear. For the free response questions, you will be graded on the quality of your answer and how serious I can tell you’ve taken the question.

5. Scan your final exam with your phone and create a PDF using Office Lens, Adobe Scan or CamScanner, all of which are free. Alternatively, you can use a standalone scanner to create a PDF using your scanner’s software. If you use any other method, then I cannot guarantee that I will be able to read your PDF.

6. Upload your exam to Teams to the ”Exam 1” assignment in the Assignments tab.

7. Do not scratch anything out. You are to produce a well-written copy of your work as a final product.

You are to give thoughtful and thorough answers to the questions. That said, I don’t want a novel. But I do want you to take them seriously and show me how you’ve grown since the start of the semester. I expect that you all will pass the exam if you give it an honest try. Good luck and be proud of how far you’ve come.

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1. (20 points) Take one homework problem you have worked on these past two weeks that you struggled to understand and solve, and explain how the struggle itself was valuable. In the context of this question, describe the struggle and how you overcame the strug- gle. You might also discuss whether struggling built aspects of character in you (e.g. endurance, self-confidence, competence to solve new problems) and how these virtues might benefit you in later ventures. Your answer should be two paragraphs, each com- prised of 4-6 sentences.

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2. (20 points) What mathematical ideas are you curious to know more about so far? Give one example of a question in the text (anywhere in the text) that you’d like to explore further, and describe why this is an interesting question to you. Your answer should be at least one paragraph (no more than two paragraphs) and each paragraph comprised of 4-6 sentences

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3. (20 points) Give one example of a mathematical idea from this class that you found creative, and explain what you find creative about it. For example, you can choose an instance of creativity you experienced in your own problem-solving, or something you read in the text. Your answer should be at least one paragraph, each paragraph comprised of 5-7 sentences (no more than two paragraphs).

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4. (20 points) Choose one interesting problem from Sections 10.1–10.3 of medium difficulty (you be the judge; no need to confirm with me) that was not assigned. Describe why you find it interesting (this is what’s important). Then solve it. Give a detailed explanation of the work involved and how you arrived at the solution. Imagine you’re teaching this problem to someone in Trigonometry. They must be able to understand and follow what you’re writing. One paragraph on why it’s interesting, with such a paragraph made up of 3-6 sentences. The length of the rest of your answer will depend on the problem you choose.

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5. (20 points) You’re stuck on a deserted island and the only way off is if you can draw one radian’s worth of rotation. How do you get off the island if all you have is a stake and a string?

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6. (20 points) In your own words, describe how to determine the height of a tree given the fact that the shadow cast by the tree is 30 meters long and the angle at which you’re looking up at the tree (from the tip of the shadow) is π/4. Show the calculations leading to the answer.

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[scratch paper]

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[scratch paper]