Q. 61 Find the exact solution of each ... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q. 61 (page 451)

Find the exact solution of each equation:
$4 \sin^{- 1} (x) = 蟺$ .

Short Answer

Expert verified

The exact solution of the equation $4 \sin^{- 1} (x) = 蟺$ is ${\frac{\sqrt{2}}{2}}$ .

Step by step solution

Step 1. Given Information.

The trigonometric equation is,

$4 \sin^{- 1} (x) = 蟺$ .

Step 2. Finding the value.

The equation is,

$4 \sin^{- 1} (x) = 蟺$

Dividing both sides by $4$ ,

$\frac{4 \sin^{- 1} (x)}{4} = \frac{蟺}{4} 鈬� \sin^{- 1} (x) = \frac{蟺}{4}$

The equation can be rewritten as,

$x = \sin (\frac{蟺}{4})$

The table of values of some common angles is,

$x$	$\frac{- 蟺}{2}$	$\frac{- 蟺}{3}$	$\frac{- 蟺}{4}$	$\frac{- 蟺}{6}$	$0$	$\frac{蟺}{6}$	$\frac{蟺}{4}$	$\frac{蟺}{3}$	$\frac{蟺}{2}$
$\sin (x)$	$- 1$	$\frac{- \sqrt{3}}{2}$	$\frac{- \sqrt{2}}{2}$	$\frac{- 1}{2}$	$0$	$\frac{1}{2}$	$\frac{\sqrt{2}}{2}$	$\frac{\sqrt{3}}{2}$	$1$

From the table, we see that when $x = \frac{蟺}{4}$ ,

$\sin (x) = \frac{\sqrt{2}}{2}$ .

The solution set is ${\frac{\sqrt{2}}{2}}$ .

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91影视

Find the exact solution of each equation:
$4 \sin^{- 1} (x) = 蟺$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Finding the value.

One App. One Place for Learning.

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91影视

Find the exact solution of each equation:4sin-1x=蟺.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Finding the value.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Logic and Functions

Mechanics Maths

Calculus

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Find the exact solution of each equation:
$4 \sin^{- 1} (x) = 蟺$ .