Let's start with the general equations of: Y=A sin (B(x-c))+D In this post, we'll talk about the B term. This term helps us find the period, the distance required to complete one cycle. It multiplies the angle. For example y=sin(90°) or in radians, y=sin (π/2) is 1. But if you make B=2 instead of 1 (not shown but assumed in the previous equation), it now looks like y=sin(2(90°) which simplifies to y=sin(2(180°). Or in radians, y=sin(2(π/2)) which simplifies to y=sin(π). These now equal...

In algebra 1 and algebra 2, the topic of one to one functions often comes up. We know that if a function is one to one, it has an inverse, which can be useful knowledge. Graphical approaches: Use horizontal and vertical line tests. Draw a vertical line through the graph and it should only intersect with function at one point. Draw a horizontal line through the graph and it should only intersect at one point. example of a function that is not one to one (fails horizontal line test): e...

Our basic y=sin (x) function looks like this, with the y axis coming in increments of 1 and the x axis coming in increments of π . Now, what happens if the coefficient of sin(x) is changed from 1 (assumed but not written) to -1?   Here's a gif of it... all the y-coordinates are now negative where they were previously positive in y=sin(x). And for y=sin(x) all y coordinates which were negative are now positive.   If we looks at a function such a...

Most students in Algebra II are comfortable using degrees, as that was typically included in their previous geometry course. Radians are an alternative way to measure angles and their refer to the length of the arc on the unit circle for a given angle. For example, a 45 degree angle corresponds to π/4 radians. Think of it like this: the circumference of a circle is 2πr and with a unit circle having a radius of 1, the circumference is 2π. Thus, a circle has 360 degrees or 2πr. Now, an 1/8 of ...

Parents often ask: What's your approach to tutoring algebra or any math subject? Having volunteered and worked as a tutor for several organizations, I use a combination of training and experience to guide my approach. Generally, I use the Socratic Method. Sometimes student simply want answers to questions but this usually isn't helpful in fostering critical thinking and understanding. If they rely on my help for everything I can't prepare them for independent learning. I ask my students qu...

Algebra 2 typically involves the study of inverse functions, among other topics. If you take a function and reflect it over the line y=x, you have its inverse. Let's take y= log(x): Now, let's add the line y=x and the inverse of y=log(x), which is y=10x. We can now see the reflection over y=x: To graph inverse functions you may simply take all the points (x,y) of the original function and swap the x coordinates for the y coordinates. For y=log(x), you can see the first two coordina...