/*! 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 5 Evaluate the expression without ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 5

Evaluate the expression without using a calculator. $$ \arcsin \frac{1}{2} $$

Short Answer

Expert verified
\(\arcsin \frac{1}{2} = \frac{\pi}{6}\)

Step by step solution

01

Understanding the Question

Here, we are finding the inverse sine of \(\frac{1}{2}\). This translates to the angle whose sine value is \(\frac{1}{2}\). If you are having trouble remembering, it could be useful to think about a right-angled triangle and the Pythagorean theorem.
02

Remembering Key Angles

We need to recall the sine values for key angles. The key angles generally include \(0, \frac{\pi}{6}, \frac{\pi}{4}, \frac{\pi}{3}, \frac{\pi}{2}\) in radians (or \(0, 30, 45, 60, 90\) degrees). We can remember that \(\sin(\frac{\pi}{6}) = \frac{1}{2}\).
03

Result

Hence, the angle whose sine value is \(\frac{1}{2}\) is \(\frac{\pi}{6}\). So, \(\arcsin \frac{1}{2} = \frac{\pi}{6}\).

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 function. Include two full periods. $$ y=\tan (x+\pi) $$

Use a graph to solve the equation on the interval \([-2 \pi, 2 \pi]\). $$ \cot x=1 $$

Evaluate the expression without using a calculator. $$ \arctan \sqrt{3} $$

Sketch the graph of the function. Include two full periods. $$ y=2 \cot \left(x+\frac{\pi}{2}\right) $$

Use the graph of the function to determine whether the function is even, odd, or neither. Verify your answer algebraically. $$ g(x)=x^{2} \cot x $$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

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.