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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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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 AA, vertical shift DD, period factor BB, and phase shift CC.

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,∞-∞,-1] ∪ [1,∞
  • Cosecant: Period 2π, range −∞,−1]∪[1,∞-∞,-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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Subjects

Pre-Calculus

Graphs

Transforming Sinusoidal Graphs

 

Pre-Calculus

•

194

•

Sep 24, 2023

•

2 pages

Fun with Unit Circle Transformations & Graphing Tricks!

user profile picture

Mira

@miraa._noui

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... Show more

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 AA, vertical shift DD, period factor BB, and phase shift CC.

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,∞-∞,-1] ∪ [1,∞
  • Cosecant: Period 2π, range −∞,−1]∪[1,∞-∞,-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 −1,1-1,1, period 2π
  • Cosine: Domain −∞,∞-∞,∞, range −1,1-1,1, period 2π, even function

Vocabulary: Transformations are expressed as gxx = ±AfB(x−C)B(x-C) + D, where:

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

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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

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I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

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Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

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iOS user

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Sudenaz Ocak

Android user

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Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

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Marco B

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Elisha

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This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

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