• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Simple Inverse trigonometry question

  • Thread starter nehcrow
  • Start date
This is a simple question but I really need to know why:

why is the alternate form of arccosh(x) = log(x + sqrt(x^2 - 1)) and not log(x - sqrt(x^2 - 1))
How do I justify the plus/minus sign?
I need to know this ASAP, thanks.
 

Mentallic

Homework Helper
3,797
94
This is a simple question but I really need to know why:

why is the alternate form of arccosh(x) = log(x + sqrt(x^2 - 1)) and not log(x - sqrt(x^2 - 1))
How do I justify the plus/minus sign?
I need to know this ASAP, thanks.
If we were to use the minus sign then [tex]0<x-\sqrt{x^2-1}<1[/tex] for [tex]x>1[/tex] and the log of this is a negative value. To have an inverse function of cosh, we need to choose one of the plus or minus, and we chose to have positive values for the arccosh function so that is why we took the plus.
 
Thank you so much!
 

Mentallic

Homework Helper
3,797
94
You're welcome :smile:
 

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top