Analytic Trigonometry - Your Complete Guide
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# 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
3.9 (7 ratings)
531 students enrolled
Last updated 4/2017
English
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Includes:
• 9.5 hours on-demand video
• 18 Articles
• 31 Supplemental Resources
• Access on mobile and TV
• Certificate of Completion
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
View Curriculum
Requirements
• Basic Arithmetic Skills
• Basic Algebra Skills
Description

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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
Preview 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