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Trigonometry

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

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

@katerevisionotes

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5 Followers

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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

305

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:

  • sin(A+B) = sinA cosB + cosA sinB
  • cos(A+B) = cosA cosB - sinA sinB

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

  • sin(2A) = 2sinA cosA
  • cos(2A) = cos²A - sin²A

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

Highlight: The R-addition formula transforms expressions of the form asinx + bcosx into Rsin(x + α) or Rcos(x + 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.

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 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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Knowunity is the #1 education app in five European countries

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Subjects

/

Maths

/

Maths pure

/

Trigonometry

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

user profile picture

Kate

@katerevisionotes

·

5 Followers

Follow

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

305

 

12/13

 

Maths

12

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

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

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(A+B) = sinA cosB + cosA sinB
  • cos(A+B) = cosA cosB - sinA sinB

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

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(x + 67.38°)

Highlight: The R-addition formula transforms expressions of the form asinx + bcosx into Rsin(x + α) or Rcos(x + 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

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

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.

Similar content

Maths - maths formulas

formulas you need to know

55

1745

3

Know maths formulas thumbnail

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

15 M

Pupils love Knowunity

#1

In education app charts in 12 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.