/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 35 Find the exact value of the give... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 35

Find the exact value of the given expression. $$ \sin ^{-1} 0 $$

Short Answer

Expert verified
The exact value of the given expression \(\sin^{-1}(0)\) is 0.

Step by step solution

01

Arcsine Definition

The inverse sine function, denoted by \(\sin^{-1}(x)\) or \(\arcsin(x)\), is the function that, given a value x in the range -1 to 1, returns the angle 胃 in the interval \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\) such that \(\sin(\theta) = x\). In other words, \(\sin^{-1}(0)\) returns an angle between \(-\frac{\pi}{2}\) and \(\frac{\pi}{2}\) whose sine is equal to 0.
02

Recall the Sine Function from the Unit Circle

On the unit circle, the sine function represents the y-coordinate value of a point, associated with an angle 胃. That is, if we know the angle 胃, we can calculate the sine value (the y-coordinate) of the point where the terminal side of the angle intersects the unit circle.
03

Identify the Angle

Now, we have to find the angle 胃 in the range of \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\) such that \(\sin(\theta) = 0\). Let's take a look at the unit circle: - When 胃 = 0, the point where the terminal side of the angle intersects the unit circle is (1,0), so \(\sin(\theta) = 0\). - Other angles in the range may not give a sine value of 0. So, \(\sin^{-1}(0) = 0\).
04

Conclusion

The exact value of the given expression, \(\sin^{-1}(0)\), is 0.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Sketch the graph of the first function by plotting points if necessary. Then use transformation(s) to obtain the graph of the second function. \(y=|x|, \quad y=|2 x-1|+1\)

The graph of the function \(f\) is to be transformed as described. Find the function for the transformed graph. \(f(x)=\sqrt{x}+1\); shifted horizontally to the left by 1 unit, compressed horizontally by a factor of 3, stretched vertically by a factor of 3, and shifted vertically downward by 2 units

Find the zero(s) of the function f to five decimal places. $$ f(x)=x^{4}-2 x^{3}+3 x-1 $$

Find the inverse of \(f .\) Then use a graphing utility to plot the graphs of \(f\) and \(f^{-1}\) using the same viewing window. $$ f(x)=\frac{x}{\sqrt{x^{2}+1}}, \quad-1 \leq x \leq 1 $$

Determine whether the function is one-to-one. $$ f(x)=-x^{4}+16 $$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.