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The equation of the tangent to a circle - higher

Easy Prigonometry: Sin, Cos, and Tan Graphs

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Easy Prigonometry: Sin, Cos, and Tan Graphs
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Scarlett

@scarletta

·

3 Followers

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A comprehensive guide to Graph analysis of sin cos tan key features, exploring the fundamental characteristics and behaviors of trigonometric functions.

  • Sine function demonstrates periodic behavior with amplitude between 1 and -1, crossing x-axis at multiples of 180°
  • Cosine function follows similar amplitude patterns but shifted 90° from sine
  • Tangent function exhibits unique characteristics with asymptotes and infinite range
  • All three functions showcase distinct crossing points, turning points, and periodic patterns
  • Understanding these graphs is crucial for advanced trigonometric analysis and applications

15/08/2023

49

Prigonometry graphs LOC 05 30 45 60 35 0 15 0.25 75 90 do 45 0.70 105 SUD 150 165 015 0.86 0.96 1 0.96 120 0.86 135 0.70 0.5 10.25 180 0 195

View

Page 2: Cosine Function Analysis

The cosine function (y = cos x) shares many similarities with sine but with a phase shift. This section explores the distinctive features of the cosine graph.

Definition: The cosine function is a periodic function with the same period as sine but shifted 90° to the left.

Key characteristics of the cosine function include:

  • X-axis crossings at 90°, 270°, and their multiples
  • Maximum value of 1 occurs at 0° and 360°
  • Minimum value of -1 occurs at 180°

Highlight: The cosine function starts at its maximum value (1) at 0°, unlike sine which starts at 0.

Prigonometry graphs LOC 05 30 45 60 35 0 15 0.25 75 90 do 45 0.70 105 SUD 150 165 015 0.86 0.96 1 0.96 120 0.86 135 0.70 0.5 10.25 180 0 195

View

Page 3: Tangent Function Analysis

This page explores Understanding tanx asymptotes and crossing points and their significance in trigonometric analysis.

Vocabulary: Asymptotes are straight lines that a curve approaches but never actually meets.

The tangent function displays unique characteristics:

  • X-axis crossings at 0°, 180°, 360°
  • Asymptotes occur at 90°, 270°, and their multiples
  • Range extends from negative infinity to positive infinity

Highlight: Unlike sine and cosine, the tangent function has no amplitude restrictions and includes vertical asymptotes.

Example: The tangent value at 45° is 1, while at 90° it approaches infinity, demonstrating the function's unbounded nature.

Prigonometry graphs LOC 05 30 45 60 35 0 15 0.25 75 90 do 45 0.70 105 SUD 150 165 015 0.86 0.96 1 0.96 120 0.86 135 0.70 0.5 10.25 180 0 195

View

Page 1: Sine Function Analysis

The sine function (y = sin x) demonstrates fundamental periodic behavior across a 360-degree cycle. This page details the comprehensive analysis of Prigonometry sin and cos graph features.

Definition: The sine function is a periodic function that repeats every 360 degrees or 2π radians.

Highlight: Key features of the sine graph include regular x-axis crossings and consistent maximum and minimum values.

The sine function exhibits several crucial characteristics:

  • X-axis crossings occur at 0°, 180°, 360° and their multiples
  • Maximum turning points occur at 90° with a value of 1
  • Minimum turning points occur at 270° with a value of -1

Example: At 30°, sin x = 0.5, demonstrating the gradual increase from 0° to the maximum at 90°.

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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.

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Knowunity is the #1 education app in five European countries

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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

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

Lena, iOS user

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Subjects

/

Maths

/

Algebra

/

Other graphs

/

The equation of the tangent to a circle - higher

Easy Prigonometry: Sin, Cos, and Tan Graphs

user profile picture

Scarlett

@scarletta

·

3 Followers

Follow

A comprehensive guide to Graph analysis of sin cos tan key features, exploring the fundamental characteristics and behaviors of trigonometric functions.

  • Sine function demonstrates periodic behavior with amplitude between 1 and -1, crossing x-axis at multiples of 180°
  • Cosine function follows similar amplitude patterns but shifted 90° from sine
  • Tangent function exhibits unique characteristics with asymptotes and infinite range
  • All three functions showcase distinct crossing points, turning points, and periodic patterns
  • Understanding these graphs is crucial for advanced trigonometric analysis and applications

15/08/2023

49

 

10/11

 

Maths

1

Prigonometry graphs LOC 05 30 45 60 35 0 15 0.25 75 90 do 45 0.70 105 SUD 150 165 015 0.86 0.96 1 0.96 120 0.86 135 0.70 0.5 10.25 180 0 195

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Page 2: Cosine Function Analysis

The cosine function (y = cos x) shares many similarities with sine but with a phase shift. This section explores the distinctive features of the cosine graph.

Definition: The cosine function is a periodic function with the same period as sine but shifted 90° to the left.

Key characteristics of the cosine function include:

  • X-axis crossings at 90°, 270°, and their multiples
  • Maximum value of 1 occurs at 0° and 360°
  • Minimum value of -1 occurs at 180°

Highlight: The cosine function starts at its maximum value (1) at 0°, unlike sine which starts at 0.

Prigonometry graphs LOC 05 30 45 60 35 0 15 0.25 75 90 do 45 0.70 105 SUD 150 165 015 0.86 0.96 1 0.96 120 0.86 135 0.70 0.5 10.25 180 0 195

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: Tangent Function Analysis

This page explores Understanding tanx asymptotes and crossing points and their significance in trigonometric analysis.

Vocabulary: Asymptotes are straight lines that a curve approaches but never actually meets.

The tangent function displays unique characteristics:

  • X-axis crossings at 0°, 180°, 360°
  • Asymptotes occur at 90°, 270°, and their multiples
  • Range extends from negative infinity to positive infinity

Highlight: Unlike sine and cosine, the tangent function has no amplitude restrictions and includes vertical asymptotes.

Example: The tangent value at 45° is 1, while at 90° it approaches infinity, demonstrating the function's unbounded nature.

Prigonometry graphs LOC 05 30 45 60 35 0 15 0.25 75 90 do 45 0.70 105 SUD 150 165 015 0.86 0.96 1 0.96 120 0.86 135 0.70 0.5 10.25 180 0 195

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: Sine Function Analysis

The sine function (y = sin x) demonstrates fundamental periodic behavior across a 360-degree cycle. This page details the comprehensive analysis of Prigonometry sin and cos graph features.

Definition: The sine function is a periodic function that repeats every 360 degrees or 2π radians.

Highlight: Key features of the sine graph include regular x-axis crossings and consistent maximum and minimum values.

The sine function exhibits several crucial characteristics:

  • X-axis crossings occur at 0°, 180°, 360° and their multiples
  • Maximum turning points occur at 90° with a value of 1
  • Minimum turning points occur at 270° with a value of -1

Example: At 30°, sin x = 0.5, demonstrating the gradual increase from 0° to the maximum at 90°.

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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.