# Simple Inverse trigonometry question

• nehcrow
In summary, the alternate form of arccosh(x) is log(x + sqrt(x^2 - 1)) instead of log(x - sqrt(x^2 - 1)) because the latter results in a negative value for the log, which is not suitable for the inverse function of cosh. The plus/minus sign is chosen for positive values of the arccosh function, making it the preferred form.
nehcrow
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.

nehcrow said:
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 $$0<x-\sqrt{x^2-1}<1$$ for $$x>1$$ 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!

You're welcome

## 1. What is inverse trigonometry?

Inverse trigonometry is the mathematical process of finding the angle measurement that produces a specific ratio of sides in a right triangle. It is the opposite of regular trigonometry, which finds the ratio of sides given an angle measurement.

## 2. How is inverse trigonometry used?

Inverse trigonometry is used to solve real-world problems involving right triangles, such as finding the height of a building or the distance between two points. It is also used in higher level math and physics to solve complex equations and models.

## 3. What are the basic inverse trigonometric functions?

The basic inverse trigonometric functions are arcsine, arccosine, and arctangent. These functions represent the inverse of sine, cosine, and tangent, respectively. They are often denoted as sin^-1, cos^-1, and tan^-1.

## 4. How do you find the inverse trigonometric value of a number?

To find the inverse trigonometric value of a number, you can use a scientific calculator or look it up in a table of trigonometric values. Alternatively, you can use the inverse trigonometric function on a graphing calculator to find the angle measure that produces the desired ratio of sides.

## 5. What is the domain and range of inverse trigonometric functions?

The domain of inverse trigonometric functions is the set of real numbers between -1 and 1, inclusive. The range is the set of all possible angle measures, typically in radians but sometimes in degrees depending on the context.

Replies
1
Views
989
Replies
5
Views
2K
Replies
12
Views
3K
Replies
3
Views
1K
Replies
44
Views
4K
Replies
10
Views
2K
Replies
10
Views
2K
Replies
2
Views
493
Replies
2
Views
926
Replies
10
Views
603