Answered: Solve the equation for x if 0 ≤ x < 2?.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Solve the equation for x if 0 ≤ x < 2?.
Use a calculator to approximate all answers to the nearest hundredth. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
7 − 4 tan(x + 3) = −9

Expert Solution

Step 1

The given equation is $7 - 4 \tan (x + 3) = - 9$ .

Solve the above equation $7 - 4 \tan (x + 3) = - 9$ for x if $0 \leq x < 2 π$ as follows.

$7 - 4 \tan (x + 3) = - 9 - 4 \tan (x + 3) = - 9 - 7 - 4 \tan (x + 3) = - 16 4 \tan (x + 3) = 16 \tan (x + 3) = 4$

Step 2

Then,

$\tan (x + 3) = 4 \Rightarrow x + 3 = \tan^{- 1} (4) + n π \Rightarrow x = \tan^{- 1} (4) + n π - 3$

When $n = 0,$

$x = \tan^{- 1} (4) - 3 \approx - 1.67 \notin [0, 2 π)$

When $n = 1,$

$x = \tan^{- 1} (4) + π - 3 \approx 1.47 \in [0, 2 π)$

When $n = 2,$

$x = \tan^{- 1} (4) + 2 π - 3 \approx 4.61 \in [0, 2 π)$

When $n = 3,$

$x = \tan^{- 1} (4) + 3 π - 3 \approx 7.75 \notin [0, 2 π)$

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