tag:blogger.com,1999:blog-56392704444067816232024-02-18T17:50:47.286-08:00Math Concepts ExplainedDo you need help in math? Easy-to-follow explanations of math topics using simple language and demonstrations. Anonymoushttp://www.blogger.com/profile/17228027233405770851noreply@blogger.comBlogger123125tag:blogger.com,1999:blog-5639270444406781623.post-70154224537148283472014-06-28T09:02:00.002-07:002014-06-28T09:02:11.852-07:00Google's Free Online CalculatorI've put up a new post over at The Numerist that talks about Google's free online calculator that is available for everyone to use and enjoy! Please visit my site to find out more, and be sure to Like it on Facebook as well! You can read my post here: http://thenumerist.com/google-free-online-calculator/Anonymoushttp://www.blogger.com/profile/17228027233405770851noreply@blogger.com0tag:blogger.com,1999:blog-5639270444406781623.post-8272444107244939592007-04-27T14:10:00.003-07:002014-06-05T11:53:42.820-07:00Trigonometry - Cosine Law, Theorem of PythagorasThe Cosine Law works similarly to the Sine Law that I have already discussed. The Cosine Law is the general form of the Pythagorean Theorem, which itself applies strictly to right angle triangles. Therefore, this law allows us to work with any triangle. It's a bit more of an equation to remember than the Sine Law unfortunately, but it is extremely useful. Here is the equation:
c(squared) = aAnonymoushttp://www.blogger.com/profile/17228027233405770851noreply@blogger.com2tag:blogger.com,1999:blog-5639270444406781623.post-12403981242924835492007-04-24T23:26:00.000-07:002014-06-05T11:53:31.345-07:00Trigonometry - Tangent, SOHCAHTOASo far, I've explained the concepts of Sine and Cosine... the third basic trigonometry function is TANGENT. If you've been following along and understanding those lessons, tangent isn't anything new for you. The tangent function of a right triangle relates an angle of the triangle to the ratio of its opposite side and its adjacent side. It does not refer to the hypotenuse at all. Referring toAnonymoushttp://www.blogger.com/profile/17228027233405770851noreply@blogger.com3tag:blogger.com,1999:blog-5639270444406781623.post-1516280451295357972007-04-27T14:10:00.001-07:002014-06-05T11:53:13.572-07:00Trigonometry - Sine Law (Law of Sines)The trig functions that I've discussed so far (Sine, Cosine, and Tangent) will be incredibly useful to you when working specifically with right angle triangles. However, of course, not all triangles have a 90 degree angle in them. So can you still use these functions? Well, yes, but in a different way. One way is through application of the Law of Sines.
Let's consider a triangle that has Anonymoushttp://www.blogger.com/profile/17228027233405770851noreply@blogger.com10tag:blogger.com,1999:blog-5639270444406781623.post-66362112861228656522010-02-26T22:09:00.000-08:002014-06-05T11:53:01.421-07:00Which Measure of Central Tendency to Use? Mode, Mean, or Median?A concept which may need a bit more explanation is: which average is appropriate for a given question? What is the best measure of central tendency? When would you use a median instead of a mean, or perhaps use a mode instead?
For any data set, you can perform the analysis to come up with a value for each average. However, here are a few basic guidelines to help you choose the most Anonymoushttp://www.blogger.com/profile/17228027233405770851noreply@blogger.com8tag:blogger.com,1999:blog-5639270444406781623.post-37476849086951608042007-06-03T19:59:00.000-07:002014-06-05T11:52:48.773-07:00Stretching Graphs and Compressing GraphsIf you understand how to shift a curve horizontally or vertically, stretching graphs or compressing them isn't much different. Once again, it's only a small modification to the equation that causes the stretch or compression. (Please click the Facebook Like button at the top of this post, or hit the Google +1 button at the end if you find this post helpful!)
Stretching and compressing Anonymoushttp://www.blogger.com/profile/17228027233405770851noreply@blogger.com8tag:blogger.com,1999:blog-5639270444406781623.post-86134000579621395162007-05-11T11:56:00.000-07:002014-06-05T11:52:39.278-07:00Trigonometry - Secant, Cosecant, CotangentIn addition to the three basic trig functions we've already looked at (Sine, Cosine, Tangent), there are three other related functions. These are Secant, Cosecant, and Cotangent. These functions have similar meanings as the first three, in that they represent the ratios of various side lengths of a right angle triangle, and can be used to find angles or unknown side lengths. I will not go intoAnonymoushttp://www.blogger.com/profile/17228027233405770851noreply@blogger.com13tag:blogger.com,1999:blog-5639270444406781623.post-23431875960036527282007-05-01T21:18:00.000-07:002014-06-05T11:52:27.015-07:00Special Angles in TrigonometrySome angles in trigonometry are so common, they are known as special angles. The values of trig functions of these specific angles can be represented by known ratios, and are good to commit to memory to help you work through problems faster. These angles can be remembered by examining two different special angle triangles. Specifically, the trig functions for angles of 0, 30, 45, 60, 90 Anonymoushttp://www.blogger.com/profile/17228027233405770851noreply@blogger.com16tag:blogger.com,1999:blog-5639270444406781623.post-68938401287856286152007-04-23T22:43:00.000-07:002014-06-05T11:52:15.350-07:00Trigonometry - Cosine, SOHCAHTOAIn continuing with my trig homework help series, this post will explain another of the basic trig functions, the cosine function.
Solving trigonometry problems that use the cosine function is extremely similar to the sine function explained in the last post. The cosine function relates an angle of a right angle triangle to the ratio of its adjacent side and the hypotenuse. The ADJACENT side toAnonymoushttp://www.blogger.com/profile/17228027233405770851noreply@blogger.com1tag:blogger.com,1999:blog-5639270444406781623.post-13919409389383520492007-04-22T18:56:00.000-07:002014-06-05T11:51:59.311-07:00Trigonometry - The Sine Function and SOHCAHTOA ExplainedSolving trigonometry problems can be easy, but it first requires you to have a solid understanding of the basic trig functions. There are three of these functions, and the first one I will discuss is SINE. I will refer to the triangle pictured in the previous post. In subsequent posts, I will highlight the other two functions: cosine and tangent.
The sine function relates an Anonymoushttp://www.blogger.com/profile/17228027233405770851noreply@blogger.com5tag:blogger.com,1999:blog-5639270444406781623.post-46858057590340947832007-04-18T14:36:00.000-07:002014-06-05T11:51:48.292-07:00What is Trigonometry?Try asking any number of young math students the question "what is trigonometry?" Inevitably, you will learn that it is one of the most feared subjects in math that students have to learn. However, solving these questions and equations is much easier than they often give it credit for. (For some interesting background history and applications of this discipline in Anonymoushttp://www.blogger.com/profile/17228027233405770851noreply@blogger.com3tag:blogger.com,1999:blog-5639270444406781623.post-37483963138194436682007-04-17T23:09:00.000-07:002014-06-05T11:51:35.274-07:00Why does "m" represent slope?Why is the symbol for slope "m"?
Few people know how to answer this question properly, which doesn't help when dealing with inquisitive students! There actually isn't a definitive answer to this question, and scholars are still looking for its first use! Unfortunately, that likely won't cure any lingering curiosity. And, frustratingly for teacher, this bit of mathematics Anonymoushttp://www.blogger.com/profile/17228027233405770851noreply@blogger.com0tag:blogger.com,1999:blog-5639270444406781623.post-18717711401683421292007-04-17T10:30:00.000-07:002014-06-05T11:51:23.512-07:00Functions - Complex, PiecewiseThe last post introduced you to functions and how they work, but there are few other things worth discussing. The first is more about function notations.
When I introduced functions, I referred to the standard notation as f(x). However, you will quickly come across problems that use different letters, but mean the same things. You will probably see things like g(x) or h(x), and they are just Anonymoushttp://www.blogger.com/profile/17228027233405770851noreply@blogger.com3tag:blogger.com,1999:blog-5639270444406781623.post-45727740424121681592007-04-09T23:50:00.000-07:002014-06-05T11:51:09.276-07:00Graphing - Standard Form of the EquationJust a short explanation for what is meant by "standard form" of the equation of the line. We have been looking at line equations in the form of y=mx+b. However, you may be asked to express this in standard form, or as a standard form equation. Graphing standard form equations will give you the exact same line as graphing something expressed as y=mx+b... standard form is just a different Anonymoushttp://www.blogger.com/profile/17228027233405770851noreply@blogger.com21tag:blogger.com,1999:blog-5639270444406781623.post-29384842695088595132013-06-01T23:09:00.000-07:002013-06-01T23:09:06.432-07:00Top 5 Most Popular Posts of MayAnother month has come and gone, so it's time to look back and tally up the page views and rank my top 5 most popular posts of May! There are few surprises once again, as it seems like my most popular material is REALLY popular, and everything else is just trying to keep up. Maybe I should consider doing a "10th place to 5th place most popular posts" write up, and maybe we'd get some different Anonymoushttp://www.blogger.com/profile/17228027233405770851noreply@blogger.com0tag:blogger.com,1999:blog-5639270444406781623.post-41759798194896150802013-05-17T22:23:00.000-07:002013-05-17T22:23:52.799-07:00Differentiation Rules - Finding the Derivative of a Difference of FunctionsThis post continues along in my series on calculus differentiation rules, this time talking about how to find the derivative of a difference of functions. I hope you read my last post, which applied to sums of functions, because it is nearly the same situation when you are subtracting. I'm not going to go into the same level as detail as I did there, so I highly recommend you go back and give Anonymoushttp://www.blogger.com/profile/17228027233405770851noreply@blogger.com0tag:blogger.com,1999:blog-5639270444406781623.post-8331326538747610912013-05-09T21:15:00.001-07:002013-05-09T21:15:21.662-07:00Differentiation Rules - Finding the Derivative of a Sum of FunctionsWelcome back to my introductory calculus series on differentiation formulas. For those who are playing along at home, I have explained several rules so far and am going to add another one today. If you've missed those posts, then I highly encourage you to go back and take a look at them to familiarize yourself with these basic concepts. (So far: here, here, and here. Or Anonymoushttp://www.blogger.com/profile/17228027233405770851noreply@blogger.com0tag:blogger.com,1999:blog-5639270444406781623.post-7414799945812263792013-04-23T20:26:00.002-07:002013-05-09T20:39:28.975-07:00Differentiation Rules - Derivative of a Constant FunctionFor those of you just tuning in, my last post was a mega-post about derivatives and an introduction to differential calculus. If you need some help getting started with understanding how to find derivatives, I highly recommend giving that a read. One impression you may have of this concept is that it requires a lot of work - lots of lengthy formulas and limit calculations. WhileAnonymoushttp://www.blogger.com/profile/17228027233405770851noreply@blogger.com0tag:blogger.com,1999:blog-5639270444406781623.post-63260234675679378562013-05-04T23:51:00.002-07:002013-05-09T20:37:40.388-07:00Differentiation Rules - Finding the Derivative of a Constant Times a FunctionIn this post I'm going to explain another one of the differentiation rules for working with derivatives. This time, I will show you how to find the derivative of a constant times a function.
In case you have missed them, I am creating a series of posts that explain some basic concepts in differential calculus. So far, in my first lesson I explained how to find the derivative of a Anonymoushttp://www.blogger.com/profile/17228027233405770851noreply@blogger.com0tag:blogger.com,1999:blog-5639270444406781623.post-69829640335446528662013-04-25T22:37:00.003-07:002013-05-09T20:32:40.021-07:00Differentiation Rules - The Power RuleWelcome to my second post of my series on differentiation formulas. So far in my recent posts, I have explored in depth all about the concept of derivatives and using differentiation to find them, and then I started this current series with an easy theorem to remember for finding the derivative of a constant function. This follow-up post will now explain to you probably one of the Anonymoushttp://www.blogger.com/profile/17228027233405770851noreply@blogger.com0tag:blogger.com,1999:blog-5639270444406781623.post-35067569410405020722013-05-08T22:26:00.000-07:002013-05-09T14:54:00.379-07:00Happy Fibonacci Day!I know this may be a little late in the day, but I just realized that today's date is actually a Fibonacci sequence! That's right, today's date is May 8, 2013, or written another way, 5/8/13!
For those who don't know, the famous Fibonacci sequence is starts off with the numbers 0, 1, and then continues by adding numbers that are equal to the sum of its preceding two numbers. So, the Anonymoushttp://www.blogger.com/profile/17228027233405770851noreply@blogger.com0tag:blogger.com,1999:blog-5639270444406781623.post-22412043791743645352012-03-08T22:42:00.003-08:002013-05-08T22:50:59.770-07:00Inverse Trigonometric Functions - Arcsine, Arccosine, ArctangentInverse trig functions are a core concept in trigonometry. Specifically, they are named arcsine, arccosine, and arctangent. We have already discussed how to find things such as the sine of 25 degrees, or cosine of 71 degrees. However, we need to introduce a new math concept to figure out such problems as "what angle gives a sine value of 0.2?" This is where inverse trig Anonymoushttp://www.blogger.com/profile/17228027233405770851noreply@blogger.com3tag:blogger.com,1999:blog-5639270444406781623.post-5900332125810258032012-02-29T22:40:00.000-08:002013-05-08T22:44:47.282-07:00Piecewise Functions ExplainedThe last post introduced you to functions and how they work, but there are few other things worth discussing - first I'll talk a bit more about function notations, and then after that, I will go over piecewise functions.
When I introduced functions, I referred to the standard notation as f(x). However, you will quickly come across problems that use different letters, but they mean the Anonymoushttp://www.blogger.com/profile/17228027233405770851noreply@blogger.com0tag:blogger.com,1999:blog-5639270444406781623.post-27294444200053252332013-04-30T21:14:00.000-07:002013-04-30T21:22:07.495-07:00Top 5 Most Popular Posts of AprilIt's that time of month again - time for a recap of my top 5 most popular posts of April! Once again, the top 5 are dominated by several of the usual favourites. However, spot number 5 is a newcomer! I'm happy to see that I have several pieces of content that are so routinely visited, but I also am very pleased to see new posts crack the top 5 as well from time to time. IfAnonymoushttp://www.blogger.com/profile/17228027233405770851noreply@blogger.com0tag:blogger.com,1999:blog-5639270444406781623.post-36761482374568297712013-04-11T23:22:00.001-07:002013-04-12T11:15:20.945-07:00Derivatives and an Introduction to Differential CalculusOne of the main concepts studied in the field of differential calculus is based on the notion of change - specifically, how one quantity changes compared to another. Perhaps a more succinct version of this physical definition would be "rate of change." Alternately, a geometric definition could simply be the slope of a curve at a particular point. The underlying key to this Anonymoushttp://www.blogger.com/profile/17228027233405770851noreply@blogger.com1