Publications by Paul Regier
Trig notes - Ch 6
6.1 Sinusoidal Graphs Plot \(f(\theta)=\sin(\theta)\). What is the domain and range of sine. What is the period of sine? Plot \(f(\theta)=\cos(\theta)\). What is the domain and range of cosine?. What is the period of cosine? Animation of sine function. Animation of cosine function. If \(f(x)\) is a function of \(x\), we say: \(f\) is even if...
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Trig - Ch. 7 Notes
7.1 Solving Trigonometric Equations with Identities Given \(f(x)=x^2+x\), solve \(f(x)=0\). Given \(f(x)= \sin^2(x) + \sin(x)\), solve \(f(x)=0\). Solve \(2\sin^2(x) + \sin(x)=0\) for all x, \(0 \leq x < 2\pi\). Solve \(3\sec^2(x) - 5 \sec(x) - 2 = 0\) for all x, \(0 \leq x < 2\pi\). Below is a reminder of all the identities we have discussed s...
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Unit 3 - Probability
1 Preliminaries Before our first meeting do the following (all free): Download and install R https://cran.r-project.org/ Download and install Desktop RStudio https://rstudio.com/products/rstudio/download/ (choose the free version) R is a free software environment for statistical computing and graphics. It compiles and runs on a wide variety of ...
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1 Intro to Probability Question: What is the difference between counting and finding probability? 1.1 Definitions When measuring discrete (whole number) outcomes, the probability of a desired outcome \(A\) is written: \[P(A) = \frac{ \text{number of outcomes in which A occurs}}{\text{total number of possible outcomes}}\] Video Question: If you r...
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1 Correct Diagnosis? Suppose a new very rare strain of COVID has an incidence rate of 0.01% (that is, it afflicts 0.01% of the population). A new test is devised to test this: Initial testing shows it produce false negatives at a rate of 0.5% (that is, 0.5% of those that have the disease will test negative), and produces false positive at a rate...
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1 Boolean Logic What is the difference between searching Google for “mystery AND comedy movies” vs “mystery OR comedy movies”? Suppose I like mystery and comedy movies, but I don’t like Halloween. What do I search for? \(~\) Boolean logic involves the classify of items into sets using keywords like: and or not Boolean logic was devel...
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Publish Document
8.1 Non-Right Triangels Law of Sines Use this picture to prove the Law of Sines. In the triangle shown here, solve for the unknown sides and angle Find the elevation of the UFO from the beginning of the section. In the triangle shown here, solve for the unknown sides and angles. When using the law of signs to solve for angles, we must be ca...
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MATH 4883 HW1
Covariance The covariance between two variables \(x\) and \(y\) is: \[Cov(x,y) =\frac{1}{n-1} \sum_{i=1}^{n} (x_i-\bar{x})(y_i-\bar{y})\] Where: \(x_i =\) the i-th data value of \(x\) \(\bar{x} =\) the mean of \(x\) \(y_i =\) the i-th data value of \(y\) \(\bar{y} =\) the mean of \(y\) \(n =\) the number of data values Find the covariance of be...
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5.1 Circles Clicker Question: Does a perfect circle exists in real life? Why or why not? A: Yes B: No way! How do you find the distance between two points on a grid? For example, find the distance between the points \((-3,2)\) and \((2,5)\)? Can you prove the Pythagorean Theorem? Can you prove the distance formula? Use the distance formula to...
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MATH 4883 - HW1
1 Finding Line Equations Find the equation of the line that passes through the points (0,-2) and (3,7). Find the equation of the line that passes through the points (-2,4) and (3,-6). 2 Finding Line of Best Fit Graph the following points: (0,8), (1,5), (2,7), and (3,4), and draw and estimate the line of best fit. Given the line of best fit fol...
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