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Chapter 4: Problem 105

Explain what is meant by one radian.

Short Answer

Expert verified
One radian is defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle. It is equivalent to approximately 57.3 degrees.

Step by step solution

01

Understanding Radian

A radian is the standard unit of angular measure used in many areas of mathematics. It is defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.
02

Relationship with Degrees

There are \(2\pi\) radians in a full circle, which is equivalent to 360 degrees. Therefore, 1 radian is approximately equal to \( \frac{360}{2\pi} \approx 57.3 \) degrees.
03

Radians in Practical Usage

In practical usage, radians are often used in fields such as physics, engineering, and computer science because they simplify certain types of calculations. For example, in physics, radians are used to express angular speeds and accelerations in terms of radians per second or radians per second squared.

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Most popular questions from this chapter

Explain how to find the length of a circular arc.

Use a vertical shift to graph one period of the function. $$y=\sin x-2$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When graphing one complete cycle of \(y=A \sin (B x-C)\) I find it easiest to begin my graph on the \(x\) -axis.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Determine the range of each of the following functions. Then give a viewing rectangle, or window, that shows two periods of the function's graph. a. \(f(x)=3 \sin \left(x+\frac{\pi}{6}\right)-2\) b. \(g(x)=\sin 3\left(x+\frac{\pi}{6}\right)-2\)

Graph one period of each function. $$y=-\left|2 \sin \frac{\pi x}{2}\right|$$
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