/*! 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 26 Evaluate \(\sin \left(\frac{\pi}... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 26

Evaluate \(\sin \left(\frac{\pi}{3}+\sin ^{-1} \frac{2}{5}\right)\).

Short Answer

Expert verified
The short answer is: \(\sin \left(\frac{\pi}{3} + \sin^{-1}\frac{2}{5}\right)\). To find this value, first evaluate \(\sin^{-1}\frac{2}{5}\), then add the result to \(\frac{\pi}{3}\), and finally compute the sine of the sum. Use a calculator or table to obtain the final answer.

Step by step solution

01

Evaluate the inverse sine of the fraction

Calculate the inverse sine of \(\frac{2}{5}\), denoted as \(\sin^{-1}\frac{2}{5}\). This value represents the angle whose sine is \(\frac{2}{5}\). Use a calculator or look it up in a table if needed.
02

Add the values inside the sine function

Add the angle in radians \(\frac{\pi}{3}\) to the angle obtained in step 1, \(\sin^{-1}\frac{2}{5}\). The combined angle is: \(\frac{\pi}{3} + \sin^{-1}\frac{2}{5}\)
03

Apply the sine function

Now, apply the sine function to the sum from step 2: \(\sin \left(\frac{\pi}{3} + \sin^{-1}\frac{2}{5}\right)\)
04

Use a calculator or table to evaluate the sine

Finally, use a calculator or a table to find the sine of the angle: \(\sin \left(\frac{\pi}{3} + \sin^{-1}\frac{2}{5}\right)\) Keep the answer accurate to an appropriate number of decimal places.

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

Give an example of an angle \(\theta\) such that \(\sin \theta\) is rational but \(\sin (2 \theta)\) is irrational.

Convert the rectangular coordinates given for each point to polar coordinates \(r\) and \(\theta .\) Use radians, and always choose the angle to be in the interval \((-\pi, \pi)\). $$ (3,-7) $$

Assume that \(f\) is the function defined by $$ f(x)=a \cos (b x+c)+d $$ Find values for \(a\) and \(d\), with \(a>0\), so that \(f\) has range [-8,6] .

What is the period of the function \(5 \cos (\pi x) ?\)

For Exercises 57-66, assume that \(f\) is the function defined by $$ f(x)=a \cos (b x+c)+d $$ Find two distinct values for \(a\) so that \(f\) has amplitude \(\frac{17}{5}\).
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

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.