Shadowing Practice: Extras ArcLength YouTube - Learn English Speaking with Video
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Have you ever heard of an arc?
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No, I’m not talking about a boat full of animals.
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I’m talking about a shape you encounter in geometry.
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An arc is a basically just part of a circle.
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In our video lesson called “Circles: What is Pi?”, you learned that a circle is the set of all points that are equidistant from a central point.
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A good way to draw a circle on the coordinate plane is to first draw a horizontal line segment from the origin to some point on the x-axis and then rotate that segment 360 degrees around the origin, leaving a trail from the endpoint as you go.
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The endpoint traces a full circle.
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But what if you don’t rotate the line a full 360 degrees?
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What if you do the same thing but only rotate it 45 degrees?
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In that case you’d only trace out a small segment of a circle.
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That’s what an arc is.
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It’s a segment of a circle’s circumference.
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And just like with a straight line segment, an arc is bound by two endpoints.
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We can make arcs of different lengths just by choosing different angles to rotate our line, which you may have realized is the radius of the full circle.
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Rotating only 10 degrees gives you this short, slightly curved line, while rotating 100 degrees gives you this much longer arc; more than one-fourth of a full circle.
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The angle you choose to rotate is called the “central angle” of the arc and it, along with the radius, determines the length of the arc.
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The bigger the central angle, the longer the arc will be.
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In fact, the distance that you’d travel if you walked along the curved path of the arc is called the “arc length”.
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That length is always longer than the distance you would walk if you traveled along a straight line between the endpoints of the arc.
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You might say that the arc takes you on a more “round-about path” haha.
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Get it? …round-about …cuz it’s a circle?
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And here’s something handy, there’s actually a formula you can use to calculate the arc length if you know the radius and the central angle of the arc.
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Let’s be clever and figure out what that formula is.
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If you rotate the radius line a full 360 degrees, the arc length would just be the same as the full circumference of the circle you make, right?
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So if we only rotate the radius line a fraction of the amount between 0 and 360, the arc length will only be a fraction of the total circumference.
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That fraction will be the angle we actually rotate the line (represented by the Greek letter theta) over the total angle for a full circumference (360 degrees).
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The formula for circumference is c = 2(Pi)r So if we just multiply that amount by the fraction (theta over 360) that should give us the arc length.
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But we should use a different letter for arc length since ‘c’ is used for a full circumference.
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Mathematicians seem to like the letter ’s’.
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Let’s try using that formula to calculate the length of an actual arc.
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Suppose we’re given an arc that was made by rotating a 4 cm long radius across a central angle of 36 degrees.
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What is its arc length?
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Well, you just substitute those values into the formula and then simplify.
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The central angle, theta, is 36 degrees and the radius is 4 centimeters.
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Simplifying, we get 36 divided by 360 is 0.1 and 2 times Pi times 4 is 8Pi.
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Pi can be estimated as 3.14 and 8 times 3.14 equals 25.12 cm.
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Finally 0.1 times 25.12 = 2.512 cm.
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Rounding off two two decimal places gives us an arc length ’s’ of 2.51 cm Okay, …hope that helps you understand what an arc is and how you can calculate its length.
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About This Lesson
In this lesson, you will gain an understanding of geometric concepts related to arcs and their lengths. You will practice articulating ideas about circles, angles, and measurements in English. Not only will you learn the vocabulary associated with these concepts, but you'll also improve your english speaking practice by shadowing the explanations. This method helps develop your pronunciation and fluency, which is essential for tasks such as IELTS speaking practice or casual conversation.
Key Vocabulary & Phrases
- Arc - A portion of the circumference of a circle.
- Central angle - The angle formed at the center of a circle by two radii.
- Arc length - The distance along the arc's curved path between two endpoints.
- Radius - A straight line from the center of a circle to any point on its circumference.
- Circumference - The total distance around a circle.
- Fraction - A numerical quantity that is not a whole number, often representing part of a whole.
- Angle - The figure formed by two rays, called the sides of the angle, sharing a common endpoint.
- Estimate - An approximate calculation or judgment about a value.
Practice Tips
To successfully enhance your english speaking practice through this lesson, consider the following shadowing techniques:
- First Listening: Play the video once without attempting to repeat. Focus on understanding the concepts presented.
- Shadowing: Play the video again, but this time, try to speak along with the narrator. Keep pace with their speed and tone, particularly when they explain vocabulary words and formulas.
- Pause & Repeat: If you find a segment challenging, pause the video, repeat what you heard, and practice speaking without looking at the transcript.
- Emphasize Key Terms: Pay attention to the pronunciation of key vocabulary and phrases. This can be crucial for effective communication during conversations or in formal situations like IELTS speaking practice.
- Record Yourself: Recording your shadow speech can help you identify areas for improvement. Listen back to your pronunciation and fluency, taking note of any words you find difficult.
Incorporating these shadow speech techniques into your study routine will enhance your grasp of both the language and the subject matter, making your learning experience more engaging and effective.
What is the Shadowing Technique?
Shadowing is a science-backed language learning technique originally developed for professional interpreter training and popularized by polyglot Dr. Alexander Arguelles. The method is simple but powerful: you listen to native English audio and immediately repeat it out loud — like a shadow following the speaker with just a 1–2 second delay. Unlike passive listening or grammar drills, shadowing forces your brain and mouth muscles to simultaneously process and reproduce real speech patterns. Research shows it significantly improves pronunciation accuracy, intonation, rhythm, connected speech, listening comprehension, and speaking fluency — making it one of the most effective methods for IELTS Speaking preparation and real-world English communication.