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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.
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Section 1: Introduction To Analytic Trigonometry  

Lecture 1 
Reference Sheet Fundamental Identites
Preview

1 page  
Section 2: The Basics for Simplifying Trigonometric Expressions  
Lecture 2  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. 

Lecture 3  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 9030 =60. This is the same for the remaining trigonometric functions. 

Lecture 4  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. 

Lecture 5  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. 

Lecture 6  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. 

Lecture 7 
What is the division property for trigonometric expressions

02:48  
Lecture 8 
How to add and subtract fractions with unlike denominators

03:39  
Section 3: Simplifying Trigonometric Expressions  
Lecture 9  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. 

Lecture 10 
Examples for simplifying trigonometric expression using trigonometric identities

09:51  
Lecture 11 
Quiz  Simplifying Trigonometric Expression(Basic)

Article  
Lecture 12 
Quiz  Simplifying Trigonometric Expression(Pythagorean Identities)

Article  
Lecture 13 
Examples for simplifying trigonometric expression by factoring

14:09  
Lecture 14 
Quiz  Simplifying Trigonometric Expression(Factoring)

Article  
Section 4: Verifying Trigonometric Identities  
Lecture 15 
Verifying Trigonometric Identities Examples 124

1 page  
Lecture 16 
Examples for verifying trigonometric identities ex 1

08:47  
Lecture 17 
Quiz  Verifying Trigonometric Identities(Basic)

Article  
Lecture 18 
Examples for verifying trigonometric identities using multiple steps

12:40  
Lecture 19 
Quiz  Verifying Trigonometric Identities(Multiple Steps)

Article  
Lecture 20 
Examples for verifying trigonometric identities using cofunction and even odd

07:17  
Lecture 21 
Quiz  Verifying Trigonometric Identities(Cofunction)

Article  
Lecture 22 
Examples for verifying trigonometric identities with rational expressions

18:51  
Lecture 23 
Quiz  Verifying Trigonometric Expression(Rational)

Article  
Lecture 24 
Essential Questions for Verifying Trigonometry Identities

1 page  
Section 5: Solving Trigonometric Equations  
Lecture 25 
Examples for solving trigonometric equations using inverse operations ex 2

13:01  
Lecture 26 
Examples for solving trigonometric equations using inverse operations ex 2

17:52  
Lecture 27 
Quiz  Solving Trigonometric Equations(Inverse Operations)

Article  
Lecture 28 
Examples for solving trigonometric equations using Pythagorean Identities

20:45  
Lecture 29 
Quiz  Solving Trigonometric Equations(Pythagorean Identities)

Article  
Lecture 30 
Examples for solving trigonometric equations using factoring

21:59  
Lecture 31 
Quiz  Solving Trigonometric Equations(Factoring)

Article  
Lecture 32 
Examples for solving trigonometric equation with two different functions

12:58  
Lecture 33 
Quiz  Solving Trigonometric Functions(Different Functions)

Article  
Lecture 34 
Examples for solving trigonometric equations with multi angles ex 1

16:20  
Lecture 35 
Examples for solving trigonometric equation with multi angles ex 2

12:30  
Lecture 36 
Quiz  Solving Trigonometric Expressions(Multiple Angles)

Article  
Section 6: Double Angle Formulas  
Lecture 37 
Examples for evaluating the double angle formulas using a triangle

07:10  
Lecture 38 
Examples for evaluating the double angle formulas for sine cosine and tangent 1

09:11  
Lecture 39 
Examples for evaluating the double angle formulas for sine cosine and tangent 2

06:06  
Lecture 40 
Examples for writing an expression as one single function using double angles

08:24  
Lecture 41 
Examples for verifying trigonometric identities using double angle formula

12:18  
Lecture 42 
Examples for solving trigonometric equations using double angle formulas

15:10  
Section 7: Half Angle Formulas  
Lecture 43 
Examples for evaluating the half angle formulas from a right triangle

07:30  
Lecture 44 
Examples for evaluating half angle formulas with constraints ex 3

10:20  
Lecture 45 
Evaluating the half angle formulas given and equation and constraint ex 2

12:19  
Lecture 46 
Examples for evaluating the half angle formulas given an equation and contraint

12:12  
Lecture 47 
Examples for evaluating the half angle formulas given an angle

12:12  
Lecture 48 
Examples for verifying trigonometric identities using half angle formulas

06:40  
Section 8: Sum and Difference Formulas  
Lecture 49 
Examples for evaluating the sum and different formulas for sine and cosine

17:04  
Lecture 50 
Examples for evaluating the sum and difference formulas for tangent

14:26  
Lecture 51 
Examples for verifying trigonometric identities using sum and difference formula

07:14  
Lecture 52 
Examples for solving trigonometric equations using sum and difference formulas

10:32  
Section 9: Oblique Triangles  
Lecture 53 
Examples for solving the missing parts of a triangle using Law of Sines AAS ASA

10:48  
Lecture 54 
Examples for determining the ambiguous case SSA (1, 2 or no triangle)

16:04  
Lecture 55 
Examples for solving the ambiguous case using Law of Sines SSA (2 cases)

13:16  
Lecture 56 
Examples for solving the missing parts of a triangle using Law of Cosines SAS

09:26  
Lecture 57 
Examples for solving the missing parts of a triangle using Law of Cosines SSS

08:50  
Lecture 58 
Examples for finding the area of an oblique triangle(Herons Formula)

06:30  
Lecture 59 
Example for determining the area of an oblique triangle

08:56  
Section 10: Vectors  
Lecture 60 
Examples for writing the vector given the initial and terminal points

10:01  
Lecture 61 
Sketching a vector

05:57  
Lecture 62 
Examples for adding, subtracting and multiplying vectors

09:47  
Lecture 63 
Examples for determining the magnitude of a vector

07:30  
Lecture 64 
Examples for determining the unit vector

06:39  
Lecture 65 
Examples for determining the dot product of two vectors

06:07  
Lecture 66 
Master Writing the vector in the same direction given the magnitude

07:14  
Lecture 67 
Examples for determining the angle of a vector

12:30  
Lecture 68 
Examples for writing the vector given the direction and magnitude

11:39  
Lecture 69 
Examples of operations of vectors including dot product

07:59  
Lecture 70 
Examples of Operations of vectors including dot product and magnitude

06:19  
Lecture 71 
Examples for determining the angle between two vectors

13:09  
Lecture 72 
Examples for determining if two vectors are orthogonal, parallel or neither

06:45 
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