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Understanding Trigonometry: Degrees, Radians, and Special Angles

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Layla Guthrie

2/16/2023

Pre-Calculus

Degrees, Radians, Coterminal Angles, and Arc Length

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Pre-Calculus

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Trigonometry

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Angle Addition Identities

Understanding Trigonometry: Degrees, Radians, and Special Angles

A comprehensive guide to trigonometric conversions and calculations, focusing on degree formats, angles, and practical applications in mathematics.

• DMS (Degrees, Minutes, Seconds) conversions and decimal degree formats are essential for precise angle measurements
• Arc length calculations involve both linear and angular measurements using radius and angle values
• Angular speed and linear speed calculations are interconnected through radius measurements
• Sector area calculations utilize radius and angle measurements in radians
• Special attention is given to coterminal angles and their practical applications

...

2/16/2023

1017

<h2 id="dmsdegreedecimal">DMS Degree Decimal</h2> <p>When converting from degrees, minutes, seconds to decimal form, it is important to reme

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Coterminal Angles and Arc Length

This section covers the relationship between coterminal angles and arc length calculations on a circle.

Definition: Coterminal angles are angles that share the same terminal side and differ by 360° or 2π radians.

Example: Finding a coterminal angle for 960°: 960° - 360° = 600° - 360° = 240°

Highlight: Arc length (S) is calculated using the formula S = rθ, where r is the radius and θ is the angle in radians.

Example: For a circle with radius 15cm and angle 105°, the arc length is: S = 15 × (105π/180) = 27.5cm

<h2 id="dmsdegreedecimal">DMS Degree Decimal</h2> <p>When converting from degrees, minutes, seconds to decimal form, it is important to reme

View

Linear and Angular Speed

This section explores the relationship between linear and angular speeds in circular motion.

Definition: Angular speed (ω) measures the rate of angular displacement, while linear speed (v) measures the actual distance traveled per unit time.

Example: For a ceiling fan rotating at 90 rpm with a 2-foot blade: Angular speed = 180π rad/min Linear speed = 1131 ft/min

Highlight: The relationship between linear and angular speed is given by v = rω, where r is the radius.

<h2 id="dmsdegreedecimal">DMS Degree Decimal</h2> <p>When converting from degrees, minutes, seconds to decimal form, it is important to reme

View

Area of Sectors and Special Applications

This section details the calculation of sector areas and introduces advanced trigonometric concepts.

Definition: The area of a sector is calculated using the formula A = ½r²θ, where θ is in radians.

Example: For a sprinkler covering 150° with a 90-foot radius: A = ½(90)²(150π/180) = 10,603 ft²

Highlight: Converting angles to radians is crucial for accurate sector area calculations.

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Subjects

Pre-Calculus

Trigonometry

Angle Addition Identities

 

Pre-Calculus

•

1,017

•

Feb 16, 2023

•

4 pages

Understanding Trigonometry: Degrees, Radians, and Special Angles

user profile picture

Layla Guthrie

@laylaguthrie_aoly

A comprehensive guide to trigonometric conversions and calculations, focusing on degree formats, angles, and practical applications in mathematics.

• DMS (Degrees, Minutes, Seconds) conversions and decimal degree formats are essential for precise angle measurements
• Arc length calculations involve both... Show more

<h2 id="dmsdegreedecimal">DMS Degree Decimal</h2> <p>When converting from degrees, minutes, seconds to decimal form, it is important to reme

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Coterminal Angles and Arc Length

This section covers the relationship between coterminal angles and arc length calculations on a circle.

Definition: Coterminal angles are angles that share the same terminal side and differ by 360° or 2π radians.

Example: Finding a coterminal angle for 960°: 960° - 360° = 600° - 360° = 240°

Highlight: Arc length (S) is calculated using the formula S = rθ, where r is the radius and θ is the angle in radians.

Example: For a circle with radius 15cm and angle 105°, the arc length is: S = 15 × (105π/180) = 27.5cm

<h2 id="dmsdegreedecimal">DMS Degree Decimal</h2> <p>When converting from degrees, minutes, seconds to decimal form, it is important to reme

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Improve your grades

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Linear and Angular Speed

This section explores the relationship between linear and angular speeds in circular motion.

Definition: Angular speed (ω) measures the rate of angular displacement, while linear speed (v) measures the actual distance traveled per unit time.

Example: For a ceiling fan rotating at 90 rpm with a 2-foot blade: Angular speed = 180π rad/min Linear speed = 1131 ft/min

Highlight: The relationship between linear and angular speed is given by v = rω, where r is the radius.

<h2 id="dmsdegreedecimal">DMS Degree Decimal</h2> <p>When converting from degrees, minutes, seconds to decimal form, it is important to reme

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Area of Sectors and Special Applications

This section details the calculation of sector areas and introduces advanced trigonometric concepts.

Definition: The area of a sector is calculated using the formula A = ½r²θ, where θ is in radians.

Example: For a sprinkler covering 150° with a 90-foot radius: A = ½(90)²(150π/180) = 10,603 ft²

Highlight: Converting angles to radians is crucial for accurate sector area calculations.

<h2 id="dmsdegreedecimal">DMS Degree Decimal</h2> <p>When converting from degrees, minutes, seconds to decimal form, it is important to reme

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

DMS and Degree Decimal Conversions

This section explains the fundamental concepts of converting between DMS (Degrees, Minutes, Seconds) and decimal degree formats, as well as transformations between degrees and radians.

Definition: DMS (Degrees, Minutes, Seconds) is a format where 1 degree equals 60 minutes, and 1 minute equals 60 seconds.

Example: Converting 74°42'15" to decimal form: 74° + 42/60° + 15/3600° = 74.7042°

Highlight: When converting from decimal degrees to DMS, multiply the decimal portion by 60 repeatedly to obtain minutes and seconds.

Vocabulary: Radians are the standard unit for angle measurement in calculus, representing the ratio of arc length to radius.

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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

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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

iOS user

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

iOS user

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