Analytic Trigonometry - Your Complete Guide

From simplifying to verifying to solving to the Law of Sines and Cosines you will learn all step by step
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  • Lectures 72
  • Contents Video: 9.5 hours
    Other: 5 mins
  • Skill Level All Levels
  • Languages English
  • Includes Lifetime access
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    Available on iOS and Android
    Certificate of Completion
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About This Course

Published 11/2013 English

Course Description

This course will take you from simplifying basic trigonometric expressions to solving complex trigonometric equations. We will sprinkle in verifying trigonometric identities in there as well. This course starts with an introductory video for each topic and then provides over 76 examples on how to solve different examples. If you need help finding the right answer each example has a step by step tutorial showing you what to do. There is also hints and processes used in the description to give you a better idea.

This course should take you a couple of days to complete while you work through the problems and use the videos as reinforcement. This course is created to be your complete guide for Analytic Trigonometry.

What are the requirements?

  • Basic Arithmetic Skills
  • Basic Algebra Skills

What am I going to get from this course?

  • Simplify, Verify, and Solve Trigonometric Equations
  • Evaluate and solve equations using the double angle formulas
  • Evaluate the verify identities using the half angle formulas
  • Evaluate and solve equations using the sum and difference formulas
  • Determine the missing parts of a triangle using Law of Sines and Law of Cosines
  • Apply operations, write and determine vectors
  • Over 200 worked out examples explained step by step
  • Over 10 quizzes to check your understanding
  • Over 30 worksheets to practice what you are learning

What is the target audience?

  • Students taking Pre-Calculus
  • Students taking Trigonometry
  • Students taking Calculus

What you get with this course?

Not for you? No problem.
30 day money back guarantee.

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Lifetime access.

Learn on the go.
Desktop, iOS and Android.

Get rewarded.
Certificate of completion.

Curriculum

Section 1: Introduction To Analytic Trigonometry
Reference Sheet Fundamental Identites
Preview
1 page
Section 2: The Basics for Simplifying Trigonometric Expressions
03:29

Remember that the reciprocal of a number such as a is 1/a and the reciprocal of a number a/b is b/a. To prove the reciprocal identities apply the functions to the values on the unit circle to confirm that they are equal to one another.

03:40

The cofunction identities can best be understood by looking at the values of your trigonometric functions within the first quadrant. You will notice that the sine of 30 degrees has the same value as the cosine of 60 degrees. This is represented in the notation of the cofunction identity as 90-30 =60. This is the same for the remaining trigonometric functions.

02:10

Remember that the quotient identities mean division. Look at a right triangle and understand that the ratio of tangent is opposite over adjacent where if that right triangle is on the unit circle the opposite side is represented by y and the adjacent side is represented by x.

02:39

Look to prove the pythagorean identities by looking at a right triangle that is within the Unit circle. The two legs are represented by sine and cosine as the hypotenuse has a length of 1. Applying the Pythagorean theorem you can prove all three Pythagorean Identities.

04:04

A basic understanding of even and odd functions as well as the graphs of the three basic trigonometric graphs is helpful in understanding the even and odd identities. Like all even functions the graph of cosine is symmetrical about the y axis so the input value will not change the output value if it is positive or negative. Similar with odd functions and sine and tangent.

What is the division property for trigonometric expressions
02:48
How to add and subtract fractions with unlike denominators
03:39
Section 3: Simplifying Trigonometric Expressions
08:05

We will break down the process and thinking that will be needed when looking at an expression to rewrite the expression in the simplest of terms possible. There is usually many routes to take to simplify an expression so practice and a solid foundation of algebraic processes will be helpful when applying the identities to simplify the expression.

Examples for simplifying trigonometric expression using trigonometric identities
09:51
Quiz - Simplifying Trigonometric Expression(Basic)
Article
Quiz - Simplifying Trigonometric Expression(Pythagorean Identities)
Article
Examples for simplifying trigonometric expression by factoring
14:09
Quiz - Simplifying Trigonometric Expression(Factoring)
Article
Section 4: Verifying Trigonometric Identities
Verifying Trigonometric Identities Examples 1-24
1 page
Examples for verifying trigonometric identities ex 1
08:47
Quiz - Verifying Trigonometric Identities(Basic)
Article
Examples for verifying trigonometric identities using multiple steps
12:40
Quiz - Verifying Trigonometric Identities(Multiple Steps)
Article
Examples for verifying trigonometric identities using co-function and even odd
07:17
Quiz - Verifying Trigonometric Identities(Co-function)
Article
Examples for verifying trigonometric identities with rational expressions
18:51
Quiz - Verifying Trigonometric Expression(Rational)
Article
Essential Questions for Verifying Trigonometry Identities
1 page
Section 5: Solving Trigonometric Equations
Examples for solving trigonometric equations using inverse operations ex 2
13:01
Examples for solving trigonometric equations using inverse operations ex 2
17:52
Quiz - Solving Trigonometric Equations(Inverse Operations)
Article
Examples for solving trigonometric equations using Pythagorean Identities
20:45
Quiz - Solving Trigonometric Equations(Pythagorean Identities)
Article
Examples for solving trigonometric equations using factoring
21:59
Quiz - Solving Trigonometric Equations(Factoring)
Article
Examples for solving trigonometric equation with two different functions
12:58
Quiz - Solving Trigonometric Functions(Different Functions)
Article
Examples for solving trigonometric equations with multi angles ex 1
16:20
Examples for solving trigonometric equation with multi angles ex 2
12:30
Quiz - Solving Trigonometric Expressions(Multiple Angles)
Article
Section 6: Double Angle Formulas
Examples for evaluating the double angle formulas using a triangle
07:10
Examples for evaluating the double angle formulas for sine cosine and tangent 1
09:11
Examples for evaluating the double angle formulas for sine cosine and tangent 2
06:06
Examples for writing an expression as one single function using double angles
08:24
Examples for verifying trigonometric identities using double angle formula
12:18
Examples for solving trigonometric equations using double angle formulas
15:10
Section 7: Half Angle Formulas
Examples for evaluating the half angle formulas from a right triangle
07:30
Examples for evaluating half angle formulas with constraints ex 3
10:20
Evaluating the half angle formulas given and equation and constraint ex 2
12:19
Examples for evaluating the half angle formulas given an equation and contraint
12:12
Examples for evaluating the half angle formulas given an angle
12:12
Examples for verifying trigonometric identities using half angle formulas
06:40
Section 8: Sum and Difference Formulas
Examples for evaluating the sum and different formulas for sine and cosine
17:04
Examples for evaluating the sum and difference formulas for tangent
14:26
Examples for verifying trigonometric identities using sum and difference formula
07:14
Examples for solving trigonometric equations using sum and difference formulas
10:32
Section 9: Oblique Triangles
Examples for solving the missing parts of a triangle using Law of Sines AAS ASA
10:48
Examples for determining the ambiguous case SSA (1, 2 or no triangle)
16:04
Examples for solving the ambiguous case using Law of Sines SSA (2 cases)
13:16
Examples for solving the missing parts of a triangle using Law of Cosines SAS
09:26
Examples for solving the missing parts of a triangle using Law of Cosines SSS
08:50
Examples for finding the area of an oblique triangle(Herons Formula)
06:30
Example for determining the area of an oblique triangle
08:56
Section 10: Vectors
Examples for writing the vector given the initial and terminal points
10:01
Sketching a vector
05:57
Examples for adding, subtracting and multiplying vectors
09:47
Examples for determining the magnitude of a vector
07:30
Examples for determining the unit vector
06:39
Examples for determining the dot product of two vectors
06:07
Master Writing the vector in the same direction given the magnitude
07:14
Examples for determining the angle of a vector
12:30
Examples for writing the vector given the direction and magnitude
11:39
Examples of operations of vectors including dot product
07:59
Examples of Operations of vectors including dot product and magnitude
06:19
Examples for determining the angle between two vectors
13:09
Examples for determining if two vectors are orthogonal, parallel or neither
06:45

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Instructor Biography

Brian McLogan, Current Active High School Math Teacher

I am a high school that is on a mission to improve math education. I was that student that sat in the back of class frustrated with the boredom of class and the lack of understanding. I made the decision to become a math teacher to make a difference in others lives. I knew that with the struggles I had I could relate well to students that struggled with math. With a weak math background I set out to get a degree in mathematics. In was a difficult journey and I worked very hard not just to pass my math classes but to have an understanding of what I was doing. I learned a lot about myself, mathematics and what it takes to be successful in class through my time at college. I want to pass along my experience to you the student so that may have your own success with mathematics.

Instructor Biography

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