Analytic Trigonometry - Your Complete Guide

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From simplifying to verifying to solving to the Law of Sines and Cosines you will learn all step by step

531 students enrolled

What Will I Learn?

- 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

Requirements

- Basic Arithmetic Skills
- Basic Algebra Skills

Description

Learning about analytic trigonometry can be tough. Once you feel you mastered one type of problem you get stumped on the next. This course is structured to not leave you behind in the dust. I start off each section with basic definitions and processes you will need to know moving through the course. I then present two types of videos to you for each skill. First is the overview video where I explain the concept as a whole like a typical lecture in a classroom. I then work through multiple examples showing you step by step how to complete different types of problems. We both know watching someone do math is not the best way to learn. You have to practice! Each section you are provided with multiple worksheets to practice your skills as well as the answer to check your answers. Revert back to videos if you get stuck and forget how to solve the problems. Once you feel you have a good grasp of your understanding it is time to take your quiz. There are multiple quizzes provided for each section. Take the quizzes as many times as you need to earn 100%. There is no pressure you are hear to learn. By taking this course you will not only gain a better understanding of analytic trigonometry but you will gain confidence to solve more problems on your own. That is why I created this course. I want students to no longer fear learning math or walking into their math class because they just don't understand. Everyone can learn math. Some it just takes a little longer, some just need a little boast and some need a course like I designed to guide them through the material. Heck once you complete this course, show your teacher! You deserve and A. I am here for you and by joining this course you are now one of my students just as important to me as the 140 students I teach in the classroom during the school year. So please keep in touch, let me know how I am doing and if there is anything extra I can provide to assist you with your learning of analytic trigonometry.

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Who is the target audience?

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

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Curriculum For This Course

79 Lectures

09:43:37
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Intro - To Analytic Geometry
1 Lecture
02:11

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The Basics for Simplifying Trigonometric Expressions
7 Lectures
22:29

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.

Preview
03:29

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.

What are the co-function identities?

03:40

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.

What are the quotient identities?

02:10

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.

What are the Pythagorean identities?

02:39

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 are the even odd identities?

04:04

What is the division property for trigonometric expressions

02:48

How to add and subtract fractions with unlike denominators

03:39

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Simplifying Trigonometric Expressions
6 Lectures
32:26

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.

Preview
08:05

Examples for simplifying trigonometric expression using trigonometric identities

09:51

Quiz - Simplifying Trigonometric Expression(Basic)

00:06

Quiz - Simplifying Trigonometric Expression(Pythagorean Identities)

00:07

Examples for simplifying trigonometric expression by factoring

14:09

Quiz - Simplifying Trigonometric Expression(Factoring)

00:07

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Verifying Trigonometric Identities
10 Lectures
48:06

Verifying Trigonometric Identities Examples 1-24

1 page

Examples for verifying trigonometric identities ex 1

08:47

Quiz - Verifying Trigonometric Identities(Basic)

00:06

Examples for verifying trigonometric identities using multiple steps

12:40

Quiz - Verifying Trigonometric Identities(Multiple Steps)

00:07

Examples for verifying trigonometric identities using co-function and even odd

07:17

Quiz - Verifying Trigonometric Identities(Co-function)

00:09

Examples for verifying trigonometric identities with rational expressions

18:51

Quiz - Verifying Trigonometric Expression(Rational)

00:06

Essential Questions for Verifying Trigonometry Identities

1 page

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Solving Trigonometric Equations
12 Lectures
01:56:05

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)

00:08

Examples for solving trigonometric equations using Pythagorean Identities

20:45

Quiz - Solving Trigonometric Equations(Pythagorean Identities)

00:08

Examples for solving trigonometric equations using factoring

21:59

Quiz - Solving Trigonometric Equations(Factoring)

00:08

Examples for solving trigonometric equation with two different functions

12:58

Quiz - Solving Trigonometric Functions(Different Functions)

00:07

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)

00:08

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Double Angle Formulas
7 Lectures
58:25

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

Quiz - Double Angle Formulas

00:06

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Half Angle Formulas
7 Lectures
01:01:19

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

Quiz - Half Angle Formulas

00:06

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Sum and Difference Formulas
6 Lectures
56:14

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

In this video you will learn how to write an expression as a single trigonometric function

Examples for writing the angle from Sum and Difference Formula

06:52

Examples for verifying trigonometric identities using sum and difference formula

07:14

Examples for solving trigonometric equations using sum and difference formulas

10:32

Quiz for Sum and Difference Formulas

00:06

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Oblique Triangles
10 Lectures
01:14:09

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

Quiz - Law of Sines

00:06

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

Quiz - Law of Cosines

00:06

Examples for finding the area of an oblique triangle(Herons Formula)

06:30

Example for determining the area of an oblique triangle

08:56

Quiz - Finding the area of an oblique triangle

00:06

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Vectors
13 Lectures
01:51:36

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

About the Instructor