How to define acos in relation to cos?

In summary, the conversation discusses the calculation of acos in relation to cos, specifically whether it can be expressed as 1/cos. The speaker originally thought it could be, but learns that it is not possible. They inquire if there is any other way to do this, but are told that acos can only be expressed as a function of other inverse trig functions. The speaker expresses surprise and disbelief, as they believed there was a relationship between acos and cos.
  • #1
Xcrypt
21
0
Hey,

Does anyone know how to calculate the formula for acos in relation to cos?

We know that cos (∏/3) = 0.5
and acos(0.5) = ∏/3

However, I assumed I could calculate acos(x) in relation to cos(x) as: 1/cos(x).
Well, I assumed wrong :(

Is there any way to do this?

Thanks
 
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  • #2
"Is there any way to do this?"

Unfortunately not. However, you can express acos as a function of any of the other inverse trig functions.
 
  • #3
Although you probably have way more experience than me in mathematics, I find your answer hard to believe...

Since acos is an inverse function of cos, they must be related in some way? If not, you just turned my whole mathematical beliefs upside down!
 

1. What is acos?

acos stands for arc cosine and is a mathematical function that returns the angle (in radians) whose cosine is the specified number.

2. How is acos related to cos?

acos and cos are inverse functions of each other. This means that acos(cos(x)) = x and cos(acos(x)) = x. In other words, acos "undoes" the cosine function.

3. How do you define acos?

To define acos, we use the formula: acos(x) = arccos(x) = cos-1(x). This means that acos is equal to the inverse cosine function.

4. What is the domain and range of acos?

The domain of acos is -1 to 1, since those are the possible values of the cosine function. The range of acos is 0 to π, or 0 to 180 degrees, since the output is an angle in radians or degrees.

5. How is acos used in real life?

acos is used in various fields such as physics, engineering, and computer science to solve problems involving angles and trigonometric functions. It is also used in GPS systems to determine the location of a device based on its distance from known points.

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