A comprehensive guide to trigonometric identities and equations examples,...
Maths356 views·Updated 21 Aug 2026·5 pagesEasy Trigonometry: Fun With Trigonometric Identities, Cosine Rule, and Quadratic Problems
Kate@katerevisionotes
1 / 5
1
of 5
Page 2: Advanced Trigonometric Functions
This page delves into transformations of trigonometric functions and essential identities.
Vocabulary: Cast diagrams are visual tools used to determine the signs of trigonometric ratios in different quadrants.
Definition: The fundamental trigonometric identity sin²θ + cos²θ = 1 forms the basis for many trigonometric proofs.
Example: When solving 2cosx = -1 in the range -180° ≤ x ≤ 540°, solutions are found at x = 120°, 240°
2
of 5
Page 3: Complex Trigonometric Applications
This section covers advanced topics including quadratic trigonometry and compound angles.
Highlight: Quadratic trigonometry factorization problems can be solved by treating trigonometric equations as standard quadratic equations.
Definition: Compound angle formulae:
- sin = sinA cosB + cosA sinB
- cos = cosA cosB - sinA sinB
Example: The equation tan²x - 2tanx = 0 can be factored as tanx = 0
3
of 5
Page 4: Double Angle Formulae and R-Addition
This page explores double angle formulae and R-addition techniques.
Definition: Double angle formulae include:
- sin(2A) = 2sinA cosA
- cos(2A) = cos²A - sin²A
Example: For R-addition formula, 5cosx - 12sinx can be written as 13cos
Highlight: The R-addition formula transforms expressions of the form asinx + bcosx into Rsin or Rcos
4
of 5
Page 5: Advanced Trigonometric Proofs
The final page focuses on complex trigonometric proofs and properties.
Example: Proving relationships involving tangent and cotangent functions requires careful manipulation of basic identities.
Highlight: Advanced proofs often involve converting expressions to simpler forms using fundamental identities.
Definition: The relationship between tangent and cotangent functions is essential for solving complex trigonometric equations.
5
of 5
Page 1: Fundamental Trigonometric Concepts
This page introduces the core concepts of trigonometry, focusing on basic ratios and rules for triangle calculations.
Definition: Trigonometric ratios are defined as relationships between sides of right-angled triangles:
- sine = opposite/hypotenuse
- cosine = adjacent/hypotenuse
- tangent = opposite/adjacent
Highlight: The cosine rule (a² = b² + c² - 2bc cosA) is essential for solving non-right angled triangles with cosine rule.
Example: Trigonometric graphs show the periodic nature of functions, with sin curves ranging between -1 and 1.
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Maths356 views·Updated 21 Aug 2026·5 pagesEasy Trigonometry: Fun With Trigonometric Identities, Cosine Rule, and Quadratic Problems
Kate@katerevisionotes
A comprehensive guide to trigonometric identities and equations examples, covering fundamental concepts and advanced applications in trigonometry.
- Explores essential trigonometric ratios (sine, cosine, tangent) and their relationships in right-angled triangles
- Details methods for solving non-right angled triangles with cosine...
1
of 5
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Page 2: Advanced Trigonometric Functions
This page delves into transformations of trigonometric functions and essential identities.
Vocabulary: Cast diagrams are visual tools used to determine the signs of trigonometric ratios in different quadrants.
Definition: The fundamental trigonometric identity sin²θ + cos²θ = 1 forms the basis for many trigonometric proofs.
Example: When solving 2cosx = -1 in the range -180° ≤ x ≤ 540°, solutions are found at x = 120°, 240°
2
of 5Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
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Page 3: Complex Trigonometric Applications
This section covers advanced topics including quadratic trigonometry and compound angles.
Highlight: Quadratic trigonometry factorization problems can be solved by treating trigonometric equations as standard quadratic equations.
Definition: Compound angle formulae:
- sin = sinA cosB + cosA sinB
- cos = cosA cosB - sinA sinB
Example: The equation tan²x - 2tanx = 0 can be factored as tanx = 0
3
of 5Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Page 4: Double Angle Formulae and R-Addition
This page explores double angle formulae and R-addition techniques.
Definition: Double angle formulae include:
- sin(2A) = 2sinA cosA
- cos(2A) = cos²A - sin²A
Example: For R-addition formula, 5cosx - 12sinx can be written as 13cos
Highlight: The R-addition formula transforms expressions of the form asinx + bcosx into Rsin or Rcos
4
of 5Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Page 5: Advanced Trigonometric Proofs
The final page focuses on complex trigonometric proofs and properties.
Example: Proving relationships involving tangent and cotangent functions requires careful manipulation of basic identities.
Highlight: Advanced proofs often involve converting expressions to simpler forms using fundamental identities.
Definition: The relationship between tangent and cotangent functions is essential for solving complex trigonometric equations.
5
of 5Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Page 1: Fundamental Trigonometric Concepts
This page introduces the core concepts of trigonometry, focusing on basic ratios and rules for triangle calculations.
Definition: Trigonometric ratios are defined as relationships between sides of right-angled triangles:
- sine = opposite/hypotenuse
- cosine = adjacent/hypotenuse
- tangent = opposite/adjacent
Highlight: The cosine rule (a² = b² + c² - 2bc cosA) is essential for solving non-right angled triangles with cosine rule.
Example: Trigonometric graphs show the periodic nature of functions, with sin curves ranging between -1 and 1.
We thought you’d never ask...
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Similar content
Most popular content: Pythagorean Identities
1Most popular content in Maths
2MathsComprehensive Maths Concepts
Explore essential mathematical concepts including powers, geometry, statistics, and probability. This resource features 65 pages of detailed explanations, diagrams, and examples to enhance your understanding of topics such as right triangles, volume calculations, and data representation. Ideal for students seeking to strengthen their numeracy skills and grasp complex mathematical principles.
1080,2326,324
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102,65261
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Explore an extensive revision of crime and deviance topics, including theories, types of crime, and the impact of media. This resource covers key concepts such as Marxism, functionalism, gender and crime, and the influence of globalization on criminal behavior. Ideal for students seeking a thorough understanding of criminology and its various theories. Type: Full Topic Revision.
1251,7111,402
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Students love us — and so will you.
4.6/5App Store
4.7/5Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan SiOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha KlichAndroid user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
AnnaiOS user