Subjects

Pre-Calculus

Trigonometry

Angle Addition Identities

Understanding Trigonometry: Degrees, Radians, and Special Angles

Name: Knowunity
Brand: Knowunity

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Understanding Trigonometry: Degrees, Radians, and Special Angles

Layla Guthrie

@laylaguthrie_aoly

219 Followers

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

985

<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

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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.

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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.

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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.

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.

Download in

Google Play

Download in

App Store

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

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 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

Subjects

Pre-Calculus

Trigonometry

Angle Addition Identities

Understanding Trigonometry: Degrees, Radians, and Special Angles

Layla Guthrie

@laylaguthrie_aoly

219 Followers

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

2/16/2023

985

Pre-Calculus

117

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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

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

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.

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

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.

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

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.

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.

Download in

Google Play

Download in

App Store

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 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