You have been evaluating trigonometric functions for values around the unit circle. Now you will use that knowledge to discover what the graph of cosine and sine look. Be sure to scale your axes with convenient values so that you can make good sketches= it matters!
11-13 AIM3 4.5 Solving Trigonometric Equations
Time to use your expanded knowledge of evaluating trigonometric functions to solve trigonometric equations. Hint: actually this is a requirement- draw unit circle right triangle to show which two quadrants you are using to solve the trigonometric equation. Use the picture on page 327 as an example. You will also see an example on the first slide in this video.
11-12 AIM3 4.4 The Pythagorean Identity
Pythagoras doing something different for us. You have started to evaluate the sine, cosine and tangent functions for any angle and now the Pythagorean Identity (what is meant by "identity" in a mathematical context?) will give us another way to do it.
11-8 AIM3 4.3 Extending the Domain
In this section you will expand upon evaluating the sine, cosine, and tangent functions for any angle. What do sin(30) and sin(390) have in common? How about cos(50) and cos(-310)?
11-5 AIM3 4.2 Extending the Domain
You now will extend upon the right triangle trigonometry you learned in previous classes. That trigonometry was, as you shall discover, limited to right triangles in the first quadrant. Now you will find the coordinates of a person walking on the unit circle, given an angle through which an observer has turned. Reminder- the 4.1 video sets up this scenario. Sure hope you watched it.
11-5 AIM3 4.1 Getting Started
There will not be a specific assignment on this section but what is covered in the video will show up again in others sections. It is important that you watch this video.
11-1 AIM3 4.0 Right Triangle Trigonometry
Chapter 4 starts several weeks of extending upon the trigonometry you met in previous classes. Understanding new concepts, definitions, and theorems will lead to success. There will also be an emphasis on drawing pictures to help visualize various concepts.
If we are on schedule this video should be watched, and notes taken, for class discussion and practice on Wednesday, November 6.
10-28 AIM3 3.13 Surveys, Studies, & Experiments
In this section you will learn how to distinguish between surveys, observational studies, and experiments. You will also learn how to recognize biased and unbiased samples and sampling techniques. Lastly, be sure you know what is so important about random sampling.
10-24 AIM3 3.12 Bernoulli Trials
How can we determine the mean, variance, and standard deviation if an experiment if we repeat it twice, or five times, or 100 times? Bernoulli to the rescue! Be sure you are clear on what exactly is a Bernoulli trial.
10-23 AIM3 3.10 Getting Started
In the next few sections you will discover how to test whether or not a statistical claim is true, and discover several methods for collecting data for statistical analysis. It will be crucial that you be able to explain the differences between these methods. Also, our friend Bernoulli makes a return to with a technique that greatly simplifies statistical analysis for a certain type of experiment. Be sure you understand what a Bernoulli trial is and the formulas associated with it.
10-22 AIM3 3.9 Repeated Experiments
The first paragraph on page 227 reminds you of some important information you met earlier and also leads us to today's discovery- consecutive trials of the same experiment will also allow you to quickly calculate important statistics. That is, if you know the mean and variance of a certain experiment, you can very easily calculate the mean and variance (and from there the standard deviation) of doing the experiment two consecutive times, or five consecutive times, or 28 consecutive times.
10-21 AIM3 3.8 Adding Variances
Big idea- means and variances from different experiments (say rolling two different dice and keeping track of the sum of the dice) can be added to find the mean and variance of the combined experiment. But, standard deviations can not be added like that. To find the SD, find the variance of the combined experiment and simply take its square root- you know, the usual relationship between variance and square root.
10-18 AIM3 3.7 Variance & Standard Deviation
Be sure to understand and memorize the formulas for variance and standard deviation. Also, note the alternative formula for the variance on page 214.
NOTE: for problem 5 use #1a as the data and let c = k = 2. This will allow you to compare your results with others in class.