Subjects

Careers

Open the App

Subjects

Easy Trigonometry: Fun With Trigonometric Identities, Cosine Rule, and Quadratic Problems

Open

12

0

user profile picture

Kate

15/09/2023

Maths

AQA Pure Math- Trigonometry- Year 1 and 2

Subjects

/

Maths

/

Maths pure

/

Trigonometry

Easy Trigonometry: Fun With Trigonometric Identities, Cosine Rule, and Quadratic Problems

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 rule and sine rule
  • Covers transformation of trigonometric functions and their graphical representations
  • Explains quadratic trigonometry factorization problems and compound angle formulae
  • Includes detailed examples of trigonometric proofs and applications
...

15/09/2023

322

T Trigonometry . • Trigonmetry opposite 0 adjacent 0 = sin() 0 = cos(a) 9: tan (8) hypotenuse 1. B non-right angled triangles. area of trian

View

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°

T Trigonometry . • Trigonmetry opposite 0 adjacent 0 = sin() 0 = cos(a) 9: tan (8) hypotenuse 1. B non-right angled triangles. area of trian

View

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:

  • sinA+BA+B = sinA cosB + cosA sinB
  • cosA+BA+B = cosA cosB - sinA sinB

Example: The equation tan²x - 2tanx = 0 can be factored as tanxtanx−2tanx - 2 = 0

T Trigonometry . • Trigonmetry opposite 0 adjacent 0 = sin() 0 = cos(a) 9: tan (8) hypotenuse 1. B non-right angled triangles. area of trian

View

Page 4: Double Angle Formulae and R-Addition

This page explores double angle formulae and R-addition techniques.

Definition: Double angle formulae include:

  • sin2A2A = 2sinA cosA
  • cos2A2A = cos²A - sin²A

Example: For R-addition formula, 5cosx - 12sinx can be written as 13cosx+67.38°x + 67.38°

Highlight: The R-addition formula transforms expressions of the form asinx + bcosx into Rsinx+αx + α or Rcosx+αx + α

T Trigonometry . • Trigonmetry opposite 0 adjacent 0 = sin() 0 = cos(a) 9: tan (8) hypotenuse 1. B non-right angled triangles. area of trian

View

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.

Similar content

Know maths formulas thumbnail

89

2616

12/13

maths formulas

formulas you need to know

Can't find what you're looking for? Explore other subjects.

Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the #1 education app in five European countries

4.9+

Average app rating

21 M

Pupils love Knowunity

#1

In education app charts in 17 countries

950 K+

Students have uploaded notes

Still not convinced? See what other students are saying...

iOS User

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

Philip, iOS User

The app is very simple and well designed. So far I have always found everything I was looking for :D

Lena, iOS user

I love this app ❤️ I actually use it every time I study.

Subjects

Maths

Maths pure

Trigonometry

 

Maths

•

322

•

15 Sept 2023

•

5 pages

Easy Trigonometry: Fun With Trigonometric Identities, Cosine Rule, and Quadratic Problems

user profile picture

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... Show more

T Trigonometry . • Trigonmetry opposite 0 adjacent 0 = sin() 0 = cos(a) 9: tan (8) hypotenuse 1. B non-right angled triangles. area of trian

Sign up to see the contentIt'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 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°

T Trigonometry . • Trigonmetry opposite 0 adjacent 0 = sin() 0 = cos(a) 9: tan (8) hypotenuse 1. B non-right angled triangles. area of trian

Sign up to see the contentIt'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 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:

  • sinA+BA+B = sinA cosB + cosA sinB
  • cosA+BA+B = cosA cosB - sinA sinB

Example: The equation tan²x - 2tanx = 0 can be factored as tanxtanx−2tanx - 2 = 0

T Trigonometry . • Trigonmetry opposite 0 adjacent 0 = sin() 0 = cos(a) 9: tan (8) hypotenuse 1. B non-right angled triangles. area of trian

Sign up to see the contentIt'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:

  • sin2A2A = 2sinA cosA
  • cos2A2A = cos²A - sin²A

Example: For R-addition formula, 5cosx - 12sinx can be written as 13cosx+67.38°x + 67.38°

Highlight: The R-addition formula transforms expressions of the form asinx + bcosx into Rsinx+αx + α or Rcosx+αx + α

T Trigonometry . • Trigonmetry opposite 0 adjacent 0 = sin() 0 = cos(a) 9: tan (8) hypotenuse 1. B non-right angled triangles. area of trian

Sign up to see the contentIt'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.

T Trigonometry . • Trigonmetry opposite 0 adjacent 0 = sin() 0 = cos(a) 9: tan (8) hypotenuse 1. B non-right angled triangles. area of trian

Sign up to see the contentIt'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+c2−2bccosAa² = 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.

Can't find what you're looking for? Explore other subjects.

Students love us — and so will you.

4.9/5

App Store

4.8/5

Google 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 S

iOS 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 Klich

Android 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.

Anna

iOS user

Best app on earth! no words because it’s too good

Thomas R

iOS user

Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.

Basil

Android user

This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.

Rohan U

Android user

I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.

Xander S

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now

Paul T

iOS user

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 S

iOS 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 Klich

Android 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.

Anna

iOS user

Best app on earth! no words because it’s too good

Thomas R

iOS user

Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.

Basil

Android user

This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.

Rohan U

Android user

I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.

Xander S

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now

Paul T

iOS user