Welcome back to the school everyone! I hope you all had a great summer. For all those whose summer was maybe a little
too great, maybe those who’ve forgotten even the basics, we’re going to take it all the way back to arithmetic a.k.a “number theory”.
A review of number theory is a perfect place to start for many levels. Calculus and a lot of what you learn in pre-calculus is based on the real number system.
When we use the word “number” we are typically referring to all real number. But how can numbers be “real”? You can’t touch the number 6 or smell 1,063. You can’t boil 1/2 or stick it in a stew. So what’s so real about real numbers? The simple answer is this:
a real number is a point on a number line (1).
-2.5 -1 0 ...
Buckle up readers, it's Trig time!
Trigonometry can be scary to many students, and in my opinion, a lot
of that is because one of the most confusing concepts in trigonometry
occurs right at the very beginning, in the form of the Unit Circle
Let's start at the beginning. Give yourself a circle with a radius of 1. Now center that circle on the origin of a coordinate plane, so that the line of the circle itself passes through the points (1,0) (0,1) (-1,0) and (0, -1). Got that?
Now, this circle is referred to as the Unit Circle, because the radius is one unit and it is therefore easier for us to do various manipulations and calculations with it.
Now choose any point on the circle (we'll call the coordinates of
that point (x,y)), draw the radius to it (which will still be a
length of 1), and drop a line back perpendicular to one of the axes.
Do that and you'll have a right triangle with the...