Simplify the there are no trigonometric expressions. following function until Sin (arcos x) =

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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**Simplify the following function until there are no trigonometric expressions.**

\[ \sin(\arccos x) = \]

To simplify \(\sin(\arccos x)\), consider a right triangle where \(\theta = \arccos x\). In this triangle:

- The adjacent side to angle \(\theta\) is \(x\).
- The hypotenuse is 1 (since the cosine is adjacent over hypotenuse).

Using the Pythagorean theorem, the opposite side, which we need for sin, is \(\sqrt{1-x^2}\).

Thus, \(\sin(\arccos x) = \sqrt{1-x^2}\).
Transcribed Image Text:**Simplify the following function until there are no trigonometric expressions.** \[ \sin(\arccos x) = \] To simplify \(\sin(\arccos x)\), consider a right triangle where \(\theta = \arccos x\). In this triangle: - The adjacent side to angle \(\theta\) is \(x\). - The hypotenuse is 1 (since the cosine is adjacent over hypotenuse). Using the Pythagorean theorem, the opposite side, which we need for sin, is \(\sqrt{1-x^2}\). Thus, \(\sin(\arccos x) = \sqrt{1-x^2}\).
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