sec2X - 4secX = 0         [ 0, 2pi )

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.2: Trigonometric Equations
Problem 15E
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sec2X - 4secX = 0         [ 0, 2pi )

I do not understand why one of the solutions is   

-arcos(1/4)

Why is it negative? If positive angles of cosine are in quadrant I and IV, I conclude that the angle is quadrant IV is...

2pi - acros(1/4)

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Trigonometry (Mind Tap Course List    ISBN: 9781337278461   10th Edition

Sec. 2.3   Prob # 68E

The explanation in Bartleby and in the textbook for the given problem is..

Solution:   - arccos (-1/4) + (2pi) (n)   ....along with other solutions...

My question:  Would I be incorrect for substituting this solution with the following: 

Solution:   2pi - acros(1/4) + (2pi) (n)

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