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Fun with Unit Circle Transformations & Graphing Tricks!

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Mira

9/24/2023

Pre-Calculus

unit circle & graphing the 6 trig functions

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Pre-Calculus

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Graphs

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Transforming Sinusoidal Graphs

Fun with Unit Circle Transformations & Graphing Tricks!

A comprehensive guide to unit circle transformations graphing techniques and trigonometric functions, covering essential concepts from basic unit circle values to complex graph transformations.

  • The unit circle serves as the foundation for understanding trigonometric functions and their values at key angles
  • Detailed coverage of writing equations for trigonometric graphs including sine, cosine, tangent, cotangent, secant, and cosecant
  • Transformation techniques explained through amplitude, period, and phase shift modifications
  • Special attention to graphing secant cosecant asymptotes and their key characteristics
  • Complete analysis of domain, range, and periodic behavior for all six trigonometric functions
...

9/24/2023

194

unit one Holdy guide THE UNIT CIRCLE T. 90 (0,1) (2. (-TE, VE 180/10 (-1,0) (글,플) I (X) BTC PE-LE 3,270 (0,-1) • (心心) (2) 1/2 12 3152 (售一些)

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Advanced Trigonometric Functions and Graph Writing

This section delves into the techniques for writing equations from graphs and understanding more complex trigonometric functions including tangent, cotangent, secant, and cosecant.

Definition: The process of writing equations involves finding amplitude (A), vertical shift (D), period factor (B), and phase shift (C).

Example: For finding amplitude: Calculate half the distance between maximum and minimum points of the graph.

Highlight: Special characteristics of advanced functions:

  • Tangent: Period π, asymptotes at x = π/2 + πk
  • Cotangent: Period π, asymptotes at x = πk
  • Secant: Period 2π, range (-∞,-1] ∪ [1,∞)
  • Cosecant: Period 2π, range (-∞,-1] ∪ [1,∞)

Vocabulary: Asymptotes are lines that a graph approaches but never touches, crucial in understanding tangent, cotangent, secant, and cosecant functions.

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Know Trig. and the Coordinate Plane Notes thumbnail

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133

11th/12th

Trig. and the Coordinate Plane Notes

Finding the six trigonometric functions on the coordinate plane and using the functions to solve triangles.

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Subjects

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Pre-Calculus

/

Graphs

/

Transforming Sinusoidal Graphs

Fun with Unit Circle Transformations & Graphing Tricks!

user profile picture

Mira

@miraa._noui

·

1,922 Followers

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A comprehensive guide to unit circle transformations graphing techniques and trigonometric functions, covering essential concepts from basic unit circle values to complex graph transformations.

  • The unit circle serves as the foundation for understanding trigonometric functions and their values at key angles
  • Detailed coverage of writing equations for trigonometric graphs including sine, cosine, tangent, cotangent, secant, and cosecant
  • Transformation techniques explained through amplitude, period, and phase shift modifications
  • Special attention to graphing secant cosecant asymptotes and their key characteristics
  • Complete analysis of domain, range, and periodic behavior for all six trigonometric functions
...

9/24/2023

194

 

11th

 

Pre-Calculus

20

unit one Holdy guide THE UNIT CIRCLE T. 90 (0,1) (2. (-TE, VE 180/10 (-1,0) (글,플) I (X) BTC PE-LE 3,270 (0,-1) • (心心) (2) 1/2 12 3152 (售一些)

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Advanced Trigonometric Functions and Graph Writing

This section delves into the techniques for writing equations from graphs and understanding more complex trigonometric functions including tangent, cotangent, secant, and cosecant.

Definition: The process of writing equations involves finding amplitude (A), vertical shift (D), period factor (B), and phase shift (C).

Example: For finding amplitude: Calculate half the distance between maximum and minimum points of the graph.

Highlight: Special characteristics of advanced functions:

  • Tangent: Period π, asymptotes at x = π/2 + πk
  • Cotangent: Period π, asymptotes at x = πk
  • Secant: Period 2π, range (-∞,-1] ∪ [1,∞)
  • Cosecant: Period 2π, range (-∞,-1] ∪ [1,∞)

Vocabulary: Asymptotes are lines that a graph approaches but never touches, crucial in understanding tangent, cotangent, secant, and cosecant functions.

unit one Holdy guide THE UNIT CIRCLE T. 90 (0,1) (2. (-TE, VE 180/10 (-1,0) (글,플) I (X) BTC PE-LE 3,270 (0,-1) • (心心) (2) 1/2 12 3152 (售一些)

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The Unit Circle and Basic Trigonometric Functions

This section covers the fundamental concepts of the unit circle and the graphing of sine and cosine functions. The unit circle is presented with its key points and angles, followed by detailed instructions for graphing basic trigonometric functions.

Definition: The unit circle is a circle with radius 1 centered at the origin, used to define trigonometric functions.

Example: To find values quickly: First draw planes with values, determine the quadrant, and for special angles like π/3 or π/6, use 30-60-90 triangle relationships.

Highlight: Sine and cosine functions have specific characteristics:

  • Sine: Domain (-∞,∞), range [-1,1], period 2π
  • Cosine: Domain (-∞,∞), range [-1,1], period 2π, even function

Vocabulary: Transformations are expressed as g(x) = ±Af[B(x-C)] + D, where:

  • A affects amplitude
  • B affects period
  • C creates phase shift
  • D creates vertical shift

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Trigonometry - Trig. and the Coordinate Plane Notes

Finding the six trigonometric functions on the coordinate plane and using the functions to solve triangles.

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133

0

Know Trig. and the Coordinate Plane Notes thumbnail

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

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and 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 ranked education app in five European countries

4.9+

Average App Rating

20 M

Students use Knowunity

#1

In Education App Charts in 17 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying