Question

Writing Read the article "Arc Length, Area and the Arcsine Function" by Andrew M. Rockett in Mathematics Magazine. Then write a paragraph explaining how the arcsine function can be defined in terms of an arc length. (To view this article, go to the website www.matharticles.com.)

Short answer

The arcsine function can be defined in terms of arc length by mapping the length of arc on the unit circle to the y-coordinate. Based on the article by Andrew M. Rockett, we understand that this connection stems from the unit circle definition where the sine function is defined geometrically as the y-coordinate of a point on the edge of the circle forming an arc. Therefore, the arcsine function, which is the inverse of the sine function, is intrinsically tied to the length of this arc.

Step-by-step solution

Access and Read the Article

Go to the website www.matharticles.com and locate the article 'Arc Length, Area and the Arcsine Function' by Andrew M. Rockett. Carefully read the article to understand its content and how the arcsine function can be defined in terms of an arc length.

Understand Key Concepts

Identify and understand key concepts related to arc lengths and the arcsine function. Note down the fundamental ideas to aid in the development of the explanation paragraph.

Develop Explanation Paragraph

Now that you have understood the content in the article, you can start developing your explanation paragraph. Keep it brief and clear, ensure it explains how the arcsine function can be defined in terms of an arc length according to the article.