FC2Video

Statistics instruction for April 7, 2009.

Statistics instruction for April 9, 2009

Normal Distributions of any mean and standard deviation are examined here.

The Normal Distribution and the Inverse Normal functions are examined. How to find z-scores or x-scores when given the probability.

Working with the Normal Distribution and the TI-84 calculator

Introduces several other common sampling techniques and discusses their properties.

Shows how to create a simple random sample using a random number table.

The definition of a simple random sample is illustrated with sets.

A further investigation into the different levels of measurement: nominal, ordinal, interval, and ratio.

What kinds of things do we measure with statistics? What kind of measurements are used?

An introduction to the concept of statistics.

We look at the idea of divisibility, factors, and the ways that different factors create the same product. 17m32s © 2008 by Raymond E. Griffith.

Divisibility rules for 7 and 13 are explored. How do we work out general rules for divisibility? 17m21s © 2008 by Raymond E. Griffith.

We look at the idea of divisibility, factors, and the ways that different factors create the same product. 17m32s © 2008 by Raymond E. Griffith.

Rules for divisibility by 2 and by 3. General divisibility rules are explored for use in proving our ideas. 17m10s © 2008 by Raymond E. Griffith.

We prove the rule for divisibility by 3, and then do divisibility by 4 and 5. 23m50s © 2008 by Raymond E. Griffith.

Finding prime numbers using the Sieve of Eratosthenes. Definition of prime and composite numbers. 14m22s

Development of the Sum and Difference formulas from cos(a+b). No formulas appear by magic, just by development from known relationships. 28m54s © 2008 by Raymond E. Griffith.

Constructing half-angle identities from double-angle identities. 29m46s © 2008 by Raymond E. Griffith.

Development of cofunction, double angle, and half-angle identities. These relationships are developed from other relationships already known. 19m01s © 2008 by Raymond E. Griffith.

Review and use of the double-angle, power-reducing, and half-angle identities. We then construct a geometric proof that the angle inscribed in a circle subtending the arc is one-half of the central angle. This will help us set up a geometric proof of the half-angle identities. 26m13s © 2008 by Raymond E. Griffith.

We develop the Pythagorean Theorem and the Distance Formula, two basic algebraic and geometric relationships. No need to take these on faith -- the reasoning behind the relationships is revealed.

Creating the formula for cos(a-b) using unit-circle positions and the distance formula from algebra. 21:49 © 2008 by Raymond E. Griffith.

Trig Identities and a review of the basics. Even after we work with trig functions for a while, we still need to be reminded of the basic identities. We finish up this one with an identity that requires use of the difference of squares from algebra. 22:00 © 2008 by Raymond E. Griffith.

The hard way and the easy way to do a problem. Even if you can't think of the easiest way to verify an identity, you can still get the job done. Later, you might see it even better. 16:30 © 2008 by Raymond E. Griffith.

Creating the formula for cos(a+b) using right-triangle trig relationships and a minimum of algebra. 26:53 © 2008 by Raymond E. Griffith.

Trig Identities and a review of the basics. Even after we work with trig functions for a while, we still need to be reminded of the basic identities. 27:30 © 2008 by Raymond E. Griffith.

Homework exercises demonstrating the verification of trig identities. Practice using the "Candice Method." We remember how to do algebra as well. 27:25 © 2008 by Raymond E. Griffith.

Homework exercises demonstrating the verification of trig identities. Practice using the "Candice Method." We remember how to do algebra as well. 26:40 © 2008 by Raymond E. Griffith.

A horrible, mean, and awful identity exercise handled in short order when we utilize factoring by grouping. A reminder that most of the problems in this section are caused by algebraic difficulties, not by trig functions. 8:23 © 2008 by Raymond E. Griffith.

A review of basic identities we will use before we start verifying trig identities. 15:46 © 2008 by Raymond E. Griffith.

Graphing transformations of tangent and cotangent. We use the graphing calculator, too. 18:36 © 2008 by Raymond E. Griffith.

Graphing transformations of the cosine function. © 2008 by Raymond E. Griffith.

We graph secant, cosecant, and tangent using sine and cosine functions. 28:14 © 2008 by Raymond E. Griffith.

Extending the graphing of trig functions. We demonstrate that the sine function looks the same despite transformations of shifting and/or stretching. We can graph the basic sine function and adjust our coordinate axes to fit the graph. 19:19 © 2008 by Raymond E. Griffith.

Graphing transformations of tangent and cotangent. We use the graphing calculator, too. 18:36 © 2008 by Raymond E. Griffith.

Extending the graphing of trig functions. We demonstrate that the sine function looks the same despite transformations of shifting and/or stretching. We can graph the basic sine function and adjust our coordinate axes to fit the graph. 25:47 © 2008 by Raymond E. Griffith.

Further discussion of even and odd functions. Development of quadrant II and quadrant III relationships. © 2008 by Raymond E. Griffith.

We examine some of the relationships between trig functions. Even/odd functions are developed for quadrants I and IV. © 2008 by Raymond E. Griffith.

Other relationships between quadrants are developed. Periodicity of functions is introduced. © 2008 by Raymond E. Griffith.

Simplifying Trig expressions. Exploring identities. Homework examples worked out. © 2008 by Raymond E. Griffith.

An introduction to characteristics of the graphs of sine and cosine functions. We use the graphing calculator and apply 171-level knowledge of function transformation to discuss properties like amplitude, period, and phase shift.

A review of the different ways we have already represented angles, triangles, and the trig functions. © 2008 by Raymond E. Griffith.

A multiple-step problem about the height and length of the skybridge between two towers. © 2008 by Raymond E. Griffith.

Applying the definitions of right triangle trigonometry, and deriving trig values. © 2008 by Raymond E. Griffith.

We look at trig functions by way of the unit circle centered on the origin of the Cartesian plane. © 2008 by Raymond E. Griffith.

Placing the right triangle on the Cartesian plane allows us to extend trig function inputs beyond 90 degrees. © 2008 by Raymond E. Griffith.

Balloons, heights of buildings, verifying the formula for the area of a triangle. © 2008 by Raymond E. Griffith.

Pulleys, gears, and rpms. © 2008 by Raymond E. Griffith.

Pulleys, gears, angular speed and rotation problems. © 2008 by Raymond E. Griffith.