Become a Trigonometry Ace

This lecture is a quick review of the necessary topics, including an overview of the xy-plane and basics about triangles.

This lecture will show you how to plot angles in the xy-plane and how to determine what quadrant an angle is in.

This lecture will show you the new measurement of angles: radians. You will also learn how to convert between degrees and radians and how to plot angles in radians.

This lecture will show you how to work with angles outside of the standard range of 0 to 360 degrees (or 0 to 2pi radians)

This lecture will show you how to compute the reference angle for any angle. A very important topic!

This lecture will show you some uses of radians. You will even be able to compute the speed (velocity) the Earth travels in space around the sun.

This lecture will show you how to memorize all the common angles on the Unit Circle with only having to know three of them using reference angles.

This lecture will define the first two trig functions: Sine and Cosine, and how to evaluate them on the angles on the Unit Circle. At the end, I mention the famous Pythagorean Identity and show you where it comes from.

This lecture will show you how to use coterminal and reference angles to evaluate sine and cosine at any angle that is coterminal to a common angle on the unit circle.

This lecture will define the other four trig functions: Secant, Cosecant, Tangent, and Cotangent. Then, using their definitions, how to evaluate each at given angles on the unit circle.

This lecture will show you how to use your calculation and definition of the trig functions to evaluate any of the six trig functions at any real number. It is important to note that your calculator will not interpret whether your angle should be in degrees or radians; you have to check the mode!

This lecture is aimed for students that have not studied right triangles or have seen the Pythagorean theorem used. These are useful tools for solving right triangles that do not require trig functions, but cannot often be used.

This lecture will show how right triangles are related to the unit circle, and we will discover how to use Sine, Cosine, and Tangent to help solve right triangles in situations where previous methods do not work.

This lecture will explain why Secant, Cosecant, and Cotangent are not really useful/necessary when solving right triangles, but how to use them if you'd like based on SOH CAH TOA.

This Lecture will show you how to apply SOH CAH TOA to word problems by drawing out pictures which form right triangles.

This lecture will show you the basis for how to graph any sine and cosine graph. Two of the four graph transformations are introduced: amplitude and midline, which go together.

This lecture will introduce the last two graph transformations important to sine and cosine graphs: Period and Horizontal shift. They often go together. You will see how changing the equation can change the period and horizontal shift.

This lecture will piece together the two previous sections. You will learn how to graph any sine or cosine graph. The important thing to notice is the steps taken are exactly the same!

This lecture will reverse the previous sections. Given a sine or cosine graph, you will learn how to identify all four of the key transformations, then use this to determine the equation of the graph.

This lecture will show you how to graph secant and cosecant graphs.

This lecture will show you how to graph tangent and cotangent functions. Most importantly, you will see the "standard" period for tangent and cotangent graphs is not the same as the other four, which is a very, very important result.

This lecture will provide background to what an inverse function does (in general), the requirements (being a one-to-one) function, then apply this specifically to our trig functions. The meaning of what an inverse trig function does is very important!

This lecture will focus on evaluating inverse trig functions. It will first be done by hand using unit circle knowledge. This will help reinforce understanding of what inverse trig functions do before you use the calculator.

This Lecture will show you how to completely finish your study of solving right triangles using inverse trig functions. SOH CAH TOA is still used. There are also a couple word problems thrown in as well.

This lecture will show you how to find and write all the angles coterminal to a given angle in a specific quadrant. A lot is review from section 1 in angles, but do not skip it! Very important for the next section.

This lecture will focus on solving basic sine and cosine equations.

This lecture will focus on solving basic tangent equations. Important note is that this is slightly different than sine or cosine equations.

This lecture will focus on expanding the previous lectures. You will learn how to solve a trig equations for all solutions with a general trig equation.

This lecture will show you how to convert general sec, csc, cot equations to their reciprocal equation with cos, sin, or cot.

This lecture will show you how to convert periodic phenomena to trig equations, then use the equation to solve questions about the phenomena.

This lecture will show you how to convert periodic phenomena to trig equations, then use the equation to solve questions about the phenomena.

This lecture will focus on understanding what the Law of Sines states and how to use it to solve triangles.

This lecture will focus on understanding the formula for the Law of Cosines and how to use it to solve triangles. At the end, I go over when to use the Law of Sines vs Law of Cosines.

This lecture will focus on applying the Law of Sines and Law of Cosines to solve word problems.

This lecture will focus on using Heron's Formula, which states how to find the area of a triangle when you know the three side lengths.

This lecture will focus on the three Pythagorean Identities and how to manipulate them.

This lecture will focus on how to use the Sum and Difference formulas for sine, cosine, and tangent.

This lecture will focus on where the double angle formulas come from and how to use them to simplify expressions.

This lecture will focus on showing how the half angle formulas come about and how to use them in a practical way (power reducing).

This lecture will focus on how to help memorize and know the practical uses of the cofunction and even-odd identities.

This lecture will focus on the uses of the sum-to-product and product-to-sum identities.

This lecture will focus on the method of how to verify/prove trig identities. As I explain in the lecture, there is no quiz since the process of these problems is what is important. The four problems in the video provide all the necessary steps to practice.

This lecture will introduce you to vectors and show how to compute their direction and magnitude.

This lecture will show you how to perform arithmetic operations on vectors and what they mean visually.

This lecture will show you how to compute the dot product of two vectors and how to use it to find the angle between two vectors.

This lecture will show you how to apply vectors to real life problems.