Subjects

Subjects

More

Search

AI Knowunity

Subjects

/

Maths

/

Pure maths

/

Trigonometry

Learn Reciprocal Trig Functions and Tricky Angles with Trigonometry!

View

Learn Reciprocal Trig Functions and Tricky Angles with Trigonometry!
user profile picture

Niamh Cooke

@niamhcooke_yelp

·

104 Followers

Follow

A comprehensive guide to fundamental trigonometry concepts and formulas, covering essential topics from basic trig ratios to compound angle formulas.

  • Explores reciprocal trig functions explanation including secant, cosecant, and cotangent
  • Details the pythagorean theorem in trigonometry and its relationship to trigonometric identities
  • Covers basic trig graphs including sine, cosine, and tangent functions
  • Presents trigonometry compound angle formulas and their applications
  • Includes special angle values (30°, 45°, 60°) and their exact trigonometric ratios
  • Explains sine and cosine rules for non-right triangles
  • Discusses transformations of trigonometric functions and radian measure

30/03/2023

142

Basic Trig. Special CasaD √2 45° Trig Graphs A 1 y=sinz g. Soke 180 360 b sin x == as & 1 line = P and ISO Frig Identities ن ال ل او ر Sон с

View

Page 2: Advanced Trigonometric Rules

This page delves into the sine and cosine rules for solving non-right triangles, along with applications in finding areas and arc lengths.

Definition: The sine rule states that a/sin A = b/sin B = c/sin C for any triangle

Example: Area of a triangle can be calculated using the formula Area = ½ab sin C

Highlight: The cosine rule (a² = b² + c² - 2bc cos A) is used when you know three sides (SSS) or two sides and the included angle (SAS)

Vocabulary: Radian measure is an alternative to degrees, where 2π radians equals 360°

Basic Trig. Special CasaD √2 45° Trig Graphs A 1 y=sinz g. Soke 180 360 b sin x == as & 1 line = P and ISO Frig Identities ن ال ل او ر Sон с

View

Page 3: Compound Angle Formulas

This page covers compound angle formulas and their applications in solving trigonometric equations.

Definition: sin(A+B) = sin A cos B + cos A sin B is a fundamental compound angle formula

Example: Double angle formulas like sin 2θ = 2sin θ cos θ are derived from compound angle formulas

Highlight: Factor formulas help simplify expressions involving sums and differences of trigonometric functions

Vocabulary: Double angle formulas are special cases of compound angle formulas where both angles are equal

Basic Trig. Special CasaD √2 45° Trig Graphs A 1 y=sinz g. Soke 180 360 b sin x == as & 1 line = P and ISO Frig Identities ن ال ل او ر Sон с

View

Page 4: Advanced Applications

This page focuses on advanced applications including r cos(θ±α) and r sin(θ±α) expressions and small angle approximations.

Definition: Small angle approximations are useful simplifications when θ is close to zero: sin θ ≈ θ, cos θ ≈ 1 - θ²/2

Example: Converting √3sin θ - cos θ to r sin(θ-α) form requires using compound angle formulas

Highlight: Maximum and minimum values of trigonometric expressions can be found using these transformations

Vocabulary: The amplitude (r) represents the maximum displacement from the midline of a trigonometric function

Basic Trig. Special CasaD √2 45° Trig Graphs A 1 y=sinz g. Soke 180 360 b sin x == as & 1 line = P and ISO Frig Identities ن ال ل او ر Sон с

View

Page 1: Basic Trigonometry Foundations

This page introduces fundamental trigonometric concepts and special angle values. The content covers basic trigonometric ratios, graphs, and identities.

Definition: The Pythagorean identity states that sin²θ + cos²θ = 1 for any angle θ.

Example: For a 45° angle, sin 45° = cos 45° = 1/√2, and tan 45° = 1

Highlight: The reciprocal trigonometric functions are derived from the basic ratios: secθ = 1/cosθ, cosecθ = 1/sinθ, and cotθ = 1/tanθ

Vocabulary: Special angles refer to commonly used angles (30°, 45°, 60°) with exact trigonometric values

Similar content

Know Exact trig values thumbnail

20

438

10/11

Exact trig values

the exact trig values with a written example of how you could used it in a question.

Know Edexel Maths Large Data Set thumbnail

42

1197

12

Edexel Maths Large Data Set

A summary covering everything included in the Edexel large data set

Know Inverse Functions notes thumbnail

5

139

S5

Inverse Functions notes

notes for higher maths on inverse functions

Know Integration Cheat Sheet thumbnail

20

610

12/13

Integration Cheat Sheet

AQA A Level maths pure revision sheet covering the integrals of a range of different functions.

Know Wave Function notes thumbnail

3

40

S5

Wave Function notes

notes for higher maths on the wave function

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.

Subjects

/

Maths

/

Pure maths

/

Trigonometry

Learn Reciprocal Trig Functions and Tricky Angles with Trigonometry!

user profile picture

Niamh Cooke

@niamhcooke_yelp

·

104 Followers

Follow

A comprehensive guide to fundamental trigonometry concepts and formulas, covering essential topics from basic trig ratios to compound angle formulas.

  • Explores reciprocal trig functions explanation including secant, cosecant, and cotangent
  • Details the pythagorean theorem in trigonometry and its relationship to trigonometric identities
  • Covers basic trig graphs including sine, cosine, and tangent functions
  • Presents trigonometry compound angle formulas and their applications
  • Includes special angle values (30°, 45°, 60°) and their exact trigonometric ratios
  • Explains sine and cosine rules for non-right triangles
  • Discusses transformations of trigonometric functions and radian measure

30/03/2023

142

 

12/13

 

Maths

9

Basic Trig. Special CasaD √2 45° Trig Graphs A 1 y=sinz g. Soke 180 360 b sin x == as & 1 line = P and ISO Frig Identities ن ال ل او ر Sон с

Sign 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 2: Advanced Trigonometric Rules

This page delves into the sine and cosine rules for solving non-right triangles, along with applications in finding areas and arc lengths.

Definition: The sine rule states that a/sin A = b/sin B = c/sin C for any triangle

Example: Area of a triangle can be calculated using the formula Area = ½ab sin C

Highlight: The cosine rule (a² = b² + c² - 2bc cos A) is used when you know three sides (SSS) or two sides and the included angle (SAS)

Vocabulary: Radian measure is an alternative to degrees, where 2π radians equals 360°

Basic Trig. Special CasaD √2 45° Trig Graphs A 1 y=sinz g. Soke 180 360 b sin x == as & 1 line = P and ISO Frig Identities ن ال ل او ر Sон с

Sign 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 3: Compound Angle Formulas

This page covers compound angle formulas and their applications in solving trigonometric equations.

Definition: sin(A+B) = sin A cos B + cos A sin B is a fundamental compound angle formula

Example: Double angle formulas like sin 2θ = 2sin θ cos θ are derived from compound angle formulas

Highlight: Factor formulas help simplify expressions involving sums and differences of trigonometric functions

Vocabulary: Double angle formulas are special cases of compound angle formulas where both angles are equal

Basic Trig. Special CasaD √2 45° Trig Graphs A 1 y=sinz g. Soke 180 360 b sin x == as & 1 line = P and ISO Frig Identities ن ال ل او ر Sон с

Sign 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: Advanced Applications

This page focuses on advanced applications including r cos(θ±α) and r sin(θ±α) expressions and small angle approximations.

Definition: Small angle approximations are useful simplifications when θ is close to zero: sin θ ≈ θ, cos θ ≈ 1 - θ²/2

Example: Converting √3sin θ - cos θ to r sin(θ-α) form requires using compound angle formulas

Highlight: Maximum and minimum values of trigonometric expressions can be found using these transformations

Vocabulary: The amplitude (r) represents the maximum displacement from the midline of a trigonometric function

Basic Trig. Special CasaD √2 45° Trig Graphs A 1 y=sinz g. Soke 180 360 b sin x == as & 1 line = P and ISO Frig Identities ن ال ل او ر Sон с

Sign 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: Basic Trigonometry Foundations

This page introduces fundamental trigonometric concepts and special angle values. The content covers basic trigonometric ratios, graphs, and identities.

Definition: The Pythagorean identity states that sin²θ + cos²θ = 1 for any angle θ.

Example: For a 45° angle, sin 45° = cos 45° = 1/√2, and tan 45° = 1

Highlight: The reciprocal trigonometric functions are derived from the basic ratios: secθ = 1/cosθ, cosecθ = 1/sinθ, and cotθ = 1/tanθ

Vocabulary: Special angles refer to commonly used angles (30°, 45°, 60°) with exact trigonometric values

Similar content

Maths - Exact trig values

the exact trig values with a written example of how you could used it in a question.

20

438

0

Know Exact trig values thumbnail

Maths - Edexel Maths Large Data Set

A summary covering everything included in the Edexel large data set

42

1197

0

Know Edexel Maths Large Data Set thumbnail

Maths - Inverse Functions notes

notes for higher maths on inverse functions

5

139

0

Know Inverse Functions notes thumbnail

Maths - Integration Cheat Sheet

AQA A Level maths pure revision sheet covering the integrals of a range of different functions.

20

610

0

Know Integration Cheat Sheet thumbnail

Maths - Wave Function notes

notes for higher maths on the wave function

3

40

0

Know Wave Function notes 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.