Precalc Problems Explained

Angles and Radians

Find out how to convert fractions of a degree with Degrees, minutes and seconds, and enter the wonderful world of the radian. I have a some examples of how to convert from degrees to radians and back again, as well as angular and linear speed using radians: Video Link

Exp and Log Functions

Video at Archive.org Video at YouTube Solving for an unknown in the exponent requires logarithms! 19 Problems are explained that involve graphing and the properties of exponents and logarithms, as well using your graphing calculator

Matrix Determinants

Matrix Determinant Video Use Cramer's Rule to solve a system of equations with Leinitz and Sarrus' method of finding the determinate of a matrix!

Fancy Trig Equations

To solve for an unknown angle we will use all sorts of clever tricks, employing the trig formulas and identities in weird and wonderful ways!

Proof of the Trig Sum and Difference Formulas

Proof of the sum and difference formulas for sine, cosine and tangent

Trig Substitution & Identities

Using the trig identities for substituting a Pythagorean looking expression.

Arithmetic Sequnces

Arithmetic Sequences

An Arithmetic Sequence is a pattern where each element changes by adding a constant. Here are examples, as well as the proof the formula for a partial sum of an arithmetic sequence.

Trig with Vectors, Complex Numbers, apps (Precalc 6)

Using the law of sines and cosines, we explor vectors, complex numbers and applications (aka "Word problems").

Using Sum & Difference Formulas

Here we find the trig functions of other angles based on the sum and difference of two angles, the double or half angle. We will prove these formulas in a different video

Some more Trig Word Problems (4.8, 4.R)

Here we use the trigonometry from our first Trig Chapter (4 in our textbook) to review how sine, cosine and tangent are used to solve word problems

Inverse Trig Functions and Trig Word Problems

Use the inverse trig functions to find unknown angles and use everything you know about sine cosine and tangent to solve word problems

Hon Algebra 2 Trig Test 1 answers

Some are getting ready for calculus by taking a Honors Algebra 2 with Trigonometry. Here are topics from Chapter 1 of the Sullivan text that are part of any Honors Algebra 2 class.

Graphing Trig Functions (4.1-4.6)

Here we have basic angles in radians, and graphing the trig functions of these angles. These functions, with their ability to transform waves with different periods and amplitudes, can be used to mathematically express all sorts of waves we find in real life. These ideas are from Sections 4.1 to 4.6 of our Precalculus book by Larsen.

Radians and Unit Circle Trig Quiz Answers

Quiz answers on radian angles, unit circle and right triangle trig (Sections 4.1-4.4)

Intro to Precalc

A broad overview of studying precalculus

Basic Algebra Review

Counting Applications

We consider how to put together our counting techniques to find out the probability of a royal flush, and figure out how many ways to give five fish to three dolphins using the partition technique.

Farkle

The old dice game "Farkle" is explained and probabilities are discussed. Special "Thank You"'s go to Br Jack, Br Chris, and all my Christian Brother buddies at Camp La Salle! See http://www.mathorama.com/farkle.html for a written summary of the rules

Binomial Theorem

Using the Binomial Theorem to expand binomials, Pascal's Rule, and an inductive proof of the Binomial Theorem. Video

Counting

Sets, Venn Diagrams, Intersections, Unions, Counting and the Multiplication Rule

Proof By Induction

An overview and three examples of proving something inductively.

Fraction Decomposition, Non-Linear Systems, Symplex Method

Answers to a Chapter 12 Test on Partial Fraction Decomposition, Non Linear Systems and the Simplex Method

Polynomial and Rational Functions

Factoring using synthetic division, and graphing techniques for polynomial and rational functions

Sarrus 3x3 Determinant Short Cut

A short-cut for finding the determinant of a 3x3 (or higher) matrix