Find the exact value of each expression. (Enter your answer in radians.) (a) arctan(1//3) (b) sin-(1)

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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**Problem Statement:**
Find the exact value of each expression. (Enter your answer in radians.)

**(a)** \(\text{arctan}\left(\frac{1}{\sqrt{3}}\right)\)

- **Answer:** \(\frac{\pi}{6}\) ✅

**(b)** \(\sin^{-1}(1)\)

- **Answer:** \(\frac{\pi}{2}\) ✅

**Explanation:**

In part (a), the expression is the arctangent of \(\frac{1}{\sqrt{3}}\). The result is \(\frac{\pi}{6}\), as this is the angle whose tangent is \(\frac{1}{\sqrt{3}}\).

In part (b), the expression is the arcsine of 1. The result is \(\frac{\pi}{2}\), as this is the angle whose sine is equal to 1.
Transcribed Image Text:**Problem Statement:** Find the exact value of each expression. (Enter your answer in radians.) **(a)** \(\text{arctan}\left(\frac{1}{\sqrt{3}}\right)\) - **Answer:** \(\frac{\pi}{6}\) ✅ **(b)** \(\sin^{-1}(1)\) - **Answer:** \(\frac{\pi}{2}\) ✅ **Explanation:** In part (a), the expression is the arctangent of \(\frac{1}{\sqrt{3}}\). The result is \(\frac{\pi}{6}\), as this is the angle whose tangent is \(\frac{1}{\sqrt{3}}\). In part (b), the expression is the arcsine of 1. The result is \(\frac{\pi}{2}\), as this is the angle whose sine is equal to 1.
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