In Exercises 31 to 39, convert the degree measure to exact radian measure. 15^∘

Name: Problem 34, Chapter 4: Essentials of Precalculus
Uploaded: 2021-07-10T19:22:55-08:00
Duration: 2 min 56 s
Channel: Chris Wojturski
Description: In Exercises 31 to 39, convert the degree measure to exact radian measure. 15^∘

In Exercises 31 to 39, convert the degree measure to exact...

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Conversion Factor

The relationship between degrees and radians is given by the conversion factor ?/180. This means that to convert an angle from degrees to radians, you multiply the degree measure by ?/180. This conversion is fundamental in linking the two units and ensuring consistency in calculations across different mathematical contexts.

Degree Measure

A degree is a unit for measuring angles, based on dividing one complete rotation into 360 equal parts. It provides a straightforward, intuitive way to describe portions of a circle and is commonly used in various fields such as geometry and trigonometry.

Radian Measure

A radian is another unit for measuring angles, defined using the radius of a circle. One radian is the measure of the angle created when the arc length equals the radius. This unit is particularly useful in higher mathematics and physics because it directly relates angles to other circular properties.

Exact Expression

When converting angles, especially when they involve common degree measures, it is often desirable to express the result in an exact form, using fractions and ? rather than a decimal approximation. This preserves mathematical precision and is important in theoretical work and proofs.

Transcript

00:02 Just like the other problems in this set, if you've been working on them, here we want to convert 15 degrees to its equivalent radian measure.

00:13 And that's easy enough to do.

00:15 And there's a lot of angle measures and radians that you'll start to see over and over again because of, you know, things like the 30, 60, 90 right triangle and the 45 -4590 right triangle.

00:26 And so you'll start to see the same types of angle measures over and over and over again.

00:33 Right now, you know, this is your first time learning about trigonometry.

00:38 You know, it's going to be a bit of a learning curve, but eventually you'll start to see the same things over and over again.

00:46 It becomes much easier.

00:47 For now, you need to remember to convert from degrees to radiance.

00:53 You have to take the angle you're given and multiply by the conversion ratio.

00:57 Which is pi over 180 degrees.

01:00 Those are the same angle measures.

01:02 So by multiplying by that, you're converting out of degrees and into radiance.

01:07 Just like if you've ever done a unit conversion, same kind of thing.

01:11 This is technically exactly the same thing.

01:14 Our units were degrees, and we're going to convert into radiance.

01:17 All right...

Please give Ace some feedback