How can I find the height of a point off the ground, using the unit circle?  For example, the radius of a circle is 8, and the center of the circle is 18 feet off the ground. How high off the ground is a point after a rotation of 11/16 pi radians

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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How can I find the height of a point off the ground, using the unit circle? 

For example, the radius of a circle is 8, and the center of the circle is 18 feet off the ground. How high off the ground is a point after a rotation of 11/16 pi radians.

 

Expert Solution
Step 1

let's take a circle with the center 'O'.

To find: - The height from the ground of the point P (x, y) lying on the circle.

Calculus homework question answer, step 1, image 1

In the above figure, we have a circle with the center at a height of 'h' from the ground.

There is a point P (x, y) at a height of h1 from the ground which after the rotation of an angle POQ(=α) reaches point Q which is at a height of h2 from the ground.

Let's say the angle between the lines OP and OX is θ, and the angle between the lines OQ and OY is θ'.

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