Technically a student coming into a Calculus class is
supposed to know both Algebra and Trigonometry. The reality is often much
different however. Most students enter a Calculus class woefully unprepared for
both the algebra and the trig that is in a Calculus class. This is very
unfortunate since good algebra skills are absolutely vital to successfully
completing any Calculus course and if your Calculus course includes trig (as
this one does) good trig skills are also important in many sections.
The intent of this chapter is to do a very cursory review
of some algebra and trig skills that are absolutely vital to a calculus course.
This chapter is not inclusive in the algebra and trig skills that are needed to
be successful in a Calculus course. It only includes those topics that most
students are particularly deficient in. For instance factoring is also vital to
completing a standard calculus class but is not included here. For a more in
depth review you should visit my Algebra/Trig review or my full set of Algebra
notes at http://tutorial.math.lamar.edu.
Note that even though these topics are very important to a
Calculus class I rarely cover all of these in the actual class itself. We
simply don’t have the time to do that. I do cover certain portions of this
chapter in class, but for the most part I leave it to the students to read this
chapter on their own.
Here is a list of topics that are in this chapter. I’ve
also denoted the sections that I typically cover during the first couple of days
of a Calculus class.
: Functions - Here
is a quick review of functions, function notation and a couple of fairly
important ideas about functions.
Review : Inverse Functions
quick review of inverse functions and the notation for inverse functions.
Trig Functions - A
review of trig functions, evaluation of trig functions and the unit circle.
This section usually gets a quick review in my class.
Review : Solving Trig Equations
reminder on how to solve trig equations. This section is always covered in my
Review : Solving Trig Equations with Calculators, Part I - The
previous section worked problem whose answers were always the “standard”
angles. In this section we work some problems whose answers are not “standard”
and so a calculator is needed. This section is always covered in my class as
most trig equations in the remainder will need a calculator.
Review : Solving Trig Equations with Calculators, Part II - Even
more trig equations requiring a calculator to solve.