/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 15 Convert each radian measure to d... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 15

Convert each radian measure to degree measure. $$ \frac{\pi}{3} $$

Short Answer

Expert verified
60掳

Step by step solution

01

Understand the Relation Between Radians and Degrees

The relationship between radians and degrees is given by \[ 180^\text{掳} = \text{蟺 radians} \]. This means that 1 radian = \[ \frac{180}{\text{蟺}} \] degrees.
02

Set Up the Conversion Formula

To convert \[ \frac{\text{蟺}}{3} \] radians to degrees, use the conversion factor \[ \frac{180^\text{掳}}{\text{蟺}} \].
03

Perform the Conversion Calculation

Multiply the radian measure by the conversion factor:\[ \frac{\text{蟺}}{3} \times \frac{180^\text{掳}}{\text{蟺}} \].
04

Simplify the Expression

Simplify the expression by canceling out 蟺:\[ \frac{180^\text{掳}}{3} \] = 60掳.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Angle Conversion
Converting between radians and degrees is a crucial skill in mathematics, especially in trigonometry. This conversion allows us to switch between two different units of measuring angles. This is handy because certain problems are easier to solve in one unit over the other.

To convert from radians to degrees, you need to use the fact that \(\text{蟺 radians}\) is equal to \(180^\text{掳}\). This relationship helps us set up a conversion factor.

For example, if you want to convert \( \frac{\text{蟺}}{3} \) radians to degrees, you use the conversion factor \( \frac{180^\text{掳}}{\text{蟺}} \). Multiply the radian measure by this factor to get your answer in degrees.
Radians
Radians are a measure of angle based on the radius of a circle. One radian is the angle created when the arc length is equal to the radius of the circle. This unit of measure is very useful in mathematics because it simplifies many equations.

To visualize what a radian is, imagine cutting a piece of string equal to the radius of a circle and then laying it along the circumference of that circle. The angle subtended by this arc length is one radian.

Mathematically, radians provide a direct relationship between the angle and the arc length, which is very useful in calculus and trigonometry.
Degrees
Degrees are another way to measure angles, more commonly seen in everyday applications. There are 360 degrees in a full circle, making degrees intuitive and easy to visualize.

For example, a right angle is \(90^\text{掳}\). This ease of visualization is part of why degrees are often used for navigation, engineering, and in most educational settings.

When converting angles from degrees to radians or vice versa, you typically use the conversion factor \( 180^\text{掳} = \text{蟺 radians} \). This is crucial for solving problems in various fields of study.

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Most popular questions from this chapter

Perform the indicated operation. Express the result in terms of \(\pi\) $$ 2 \pi-\frac{\pi}{3} $$

Convert \(13 \pi / 12\) radians to degree measure.

Solve each problem. In each case name the quadrant containing the terminal side of \(2 \alpha\) a. \(\alpha=66^{\circ}\) b. \(\alpha=2 \pi / 3\) c. \(\alpha=150^{\circ}\) d. \(\alpha=-5 \pi / 6\)

Photographing Earth From an altitude of \(161 \mathrm{mi},\) the Orbiting Geophysical Observatory (OGO-1) can photograph a path on the surface of Earth that is approximately \(2000 \mathrm{mi}\) wide. Find the central angle, to the nearest tenth of a degree, that intercepts an arc of 2000 mi on the surface of Earth (radius \(3950 \mathrm{mi}\) )

True or false? Do not use a calculator. $$ \cos \left(150^{\circ}\right)=-\cos \left(30^{\circ}\right) $$
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