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Let's Learn: Solving Right Triangles and Understanding Vectors

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Jessica Lindeman

2/12/2023

Physics

Math Review for Vectors

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Energy and Fields

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Energy and Fields

Let's Learn: Solving Right Triangles and Understanding Vectors

Solving right triangles using Pythagorean theorem and Understanding vector components in physics form the foundation of this comprehensive math review for vectors in Physics 421.

• The document covers essential mathematical concepts including the Pythagorean theorem, trigonometric ratios, and vector analysis
• Detailed explanations of vector components, resolution, and addition are provided with practical examples
• Special emphasis is placed on trigonometric values in triangle labeling and solving real-world physics problems
• The material progresses from basic right triangle calculations to complex vector addition scenarios

...

2/12/2023

194

Name: Jessica Lindeman tr Period: atMath Review for Vectors mit gnivollot stil toda Physics 421 Pythagorean Theorem- Relationship between th

View

Page 2: Trigonometric Ratios

The second page explores basic trigonometric ratios and their applications in right triangles, introducing sine, cosine, and tangent relationships.

Vocabulary:

  • Sine sinθsin θ = opposite/hypotenuse
  • Cosine cosθcos θ = adjacent/hypotenuse
  • Tangent tanθtan θ = opposite/adjacent

Example: In a right triangle with sides 3, 4, and 5 units, sin C = 3/5, cos C = 4/5, and tan C = 3/4.

Name: Jessica Lindeman tr Period: atMath Review for Vectors mit gnivollot stil toda Physics 421 Pythagorean Theorem- Relationship between th

View

Page 3: Introduction to Vectors

This page introduces vector concepts and their fundamental properties in physics, including definition and representation methods.

Definition: A vector is a quantity that has both magnitude and direction.

Highlight: Vector components can be broken down into x and y components parallel to the coordinate axes.

Example: Angles can be measured either counterclockwise from the positive x-axis or as degrees above/below the x-axis.

Name: Jessica Lindeman tr Period: atMath Review for Vectors mit gnivollot stil toda Physics 421 Pythagorean Theorem- Relationship between th

View

Page 4: Vector Components

Detailed explanation of vector component calculations using trigonometric functions, with practical applications.

Example: A plane flying at 123 km/h at 40° above the x-axis has components:

  • X-component = 123 cos40°40° = 94.2 km/h
  • Y-component = 123 sin40°40° = 79.1 km/h

Highlight: Component calculations rely on cosine for x-components and sine for y-components.

Name: Jessica Lindeman tr Period: atMath Review for Vectors mit gnivollot stil toda Physics 421 Pythagorean Theorem- Relationship between th

View

Page 5: Vector Component Practice

This page provides practice problems for calculating vector components with negative angles and forces.

Example: For 18 km at 47° below the positive x-axis:

  • X-component = 18 cos47°47° = 12.3 km
  • Y-component = 18 sin47°47° = -13.1 km
Name: Jessica Lindeman tr Period: atMath Review for Vectors mit gnivollot stil toda Physics 421 Pythagorean Theorem- Relationship between th

View

Page 6: Vector Addition

Introduction to vector addition methods and resultant vector calculations.

Definition: The resultant vector is the single vector that has the same effect as two or more vectors acting together.

Example: Adding 20 N East and 7 N North vectors results in a 21.2 N resultant at 19.3° above the positive x-axis.

Name: Jessica Lindeman tr Period: atMath Review for Vectors mit gnivollot stil toda Physics 421 Pythagorean Theorem- Relationship between th

View

Page 7: Advanced Vector Addition

Comprehensive coverage of vector addition problem-solving methodology with multiple examples.

Highlight: Four key steps for vector addition:

  1. Sketch and resolve each vector
  2. Add x and y components
  3. Draw resultant triangle
  4. Calculate magnitude and direction

Example: Adding vectors of 4.0m 90° below x-axis and 8.3m 55° above negative x-axis results in 5.6m at 30.3° above negative x-axis.

Name: Jessica Lindeman tr Period: atMath Review for Vectors mit gnivollot stil toda Physics 421 Pythagorean Theorem- Relationship between th

View

Page 7: Vector Addition Methods

This page outlines the systematic approach to vector addition problems.

Definition: Four key steps for solving vector addition problems are presented:

  1. Sketch and resolve vectors
  2. Add x and y components
  3. Draw component triangle
  4. Calculate resultant magnitude and direction

Example: Addition of vectors including 20 N along positive x-axis and another at 30° above.

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Subjects

Physics

Energy and Fields

Energy and Fields

 

Physics

•

194

•

Feb 12, 2023

•

8 pages

Let's Learn: Solving Right Triangles and Understanding Vectors

user profile picture

Jessica Lindeman

@jessicalindeman_cszz

Solving right triangles using Pythagorean theorem and Understanding vector components in physics form the foundation of this comprehensive math review for vectors in Physics 421.

• The document covers essential mathematical concepts including the Pythagorean theorem, trigonometric ratios, and vector... Show more

Name: Jessica Lindeman tr Period: atMath Review for Vectors mit gnivollot stil toda Physics 421 Pythagorean Theorem- Relationship between th

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Page 2: Trigonometric Ratios

The second page explores basic trigonometric ratios and their applications in right triangles, introducing sine, cosine, and tangent relationships.

Vocabulary:

  • Sine sinθsin θ = opposite/hypotenuse
  • Cosine cosθcos θ = adjacent/hypotenuse
  • Tangent tanθtan θ = opposite/adjacent

Example: In a right triangle with sides 3, 4, and 5 units, sin C = 3/5, cos C = 4/5, and tan C = 3/4.

Name: Jessica Lindeman tr Period: atMath Review for Vectors mit gnivollot stil toda Physics 421 Pythagorean Theorem- Relationship between th

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Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 3: Introduction to Vectors

This page introduces vector concepts and their fundamental properties in physics, including definition and representation methods.

Definition: A vector is a quantity that has both magnitude and direction.

Highlight: Vector components can be broken down into x and y components parallel to the coordinate axes.

Example: Angles can be measured either counterclockwise from the positive x-axis or as degrees above/below the x-axis.

Name: Jessica Lindeman tr Period: atMath Review for Vectors mit gnivollot stil toda Physics 421 Pythagorean Theorem- Relationship between th

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Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 4: Vector Components

Detailed explanation of vector component calculations using trigonometric functions, with practical applications.

Example: A plane flying at 123 km/h at 40° above the x-axis has components:

  • X-component = 123 cos40°40° = 94.2 km/h
  • Y-component = 123 sin40°40° = 79.1 km/h

Highlight: Component calculations rely on cosine for x-components and sine for y-components.

Name: Jessica Lindeman tr Period: atMath Review for Vectors mit gnivollot stil toda Physics 421 Pythagorean Theorem- Relationship between th

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

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Page 5: Vector Component Practice

This page provides practice problems for calculating vector components with negative angles and forces.

Example: For 18 km at 47° below the positive x-axis:

  • X-component = 18 cos47°47° = 12.3 km
  • Y-component = 18 sin47°47° = -13.1 km
Name: Jessica Lindeman tr Period: atMath Review for Vectors mit gnivollot stil toda Physics 421 Pythagorean Theorem- Relationship between th

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Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 6: Vector Addition

Introduction to vector addition methods and resultant vector calculations.

Definition: The resultant vector is the single vector that has the same effect as two or more vectors acting together.

Example: Adding 20 N East and 7 N North vectors results in a 21.2 N resultant at 19.3° above the positive x-axis.

Name: Jessica Lindeman tr Period: atMath Review for Vectors mit gnivollot stil toda Physics 421 Pythagorean Theorem- Relationship between th

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Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 7: Advanced Vector Addition

Comprehensive coverage of vector addition problem-solving methodology with multiple examples.

Highlight: Four key steps for vector addition:

  1. Sketch and resolve each vector
  2. Add x and y components
  3. Draw resultant triangle
  4. Calculate magnitude and direction

Example: Adding vectors of 4.0m 90° below x-axis and 8.3m 55° above negative x-axis results in 5.6m at 30.3° above negative x-axis.

Name: Jessica Lindeman tr Period: atMath Review for Vectors mit gnivollot stil toda Physics 421 Pythagorean Theorem- Relationship between th

Sign up to see the contentIt'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 7: Vector Addition Methods

This page outlines the systematic approach to vector addition problems.

Definition: Four key steps for solving vector addition problems are presented:

  1. Sketch and resolve vectors
  2. Add x and y components
  3. Draw component triangle
  4. Calculate resultant magnitude and direction

Example: Addition of vectors including 20 N along positive x-axis and another at 30° above.

Name: Jessica Lindeman tr Period: atMath Review for Vectors mit gnivollot stil toda Physics 421 Pythagorean Theorem- Relationship between th

Sign up to see the contentIt'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: Pythagorean Theorem Review

This page introduces the fundamental relationship between sides of a right triangle using the Pythagorean theorem. The content focuses on practical problem-solving using the formula a² + b² = c².

Definition: The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides.

Example: A right triangle with sides 8 and 6 units has its hypotenuse calculated as √64+3664 + 36 = 10 units.

Highlight: The formula a² + b² = c² is essential for solving unknown sides in right triangles.

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Paul T

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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

iOS user

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

iOS user

Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

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🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

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

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

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THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

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

iOS user