How to define acos in relation to cos?

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SUMMARY

The discussion centers on the relationship between the inverse cosine function, acos, and the cosine function, cos. It is established that while cos(π/3) equals 0.5, the expression for acos(0.5) is π/3. The misconception that acos(x) can be calculated as 1/cos(x) is clarified as incorrect. Participants confirm that acos cannot be directly expressed in terms of cos, but it can be related to other inverse trigonometric functions.

PREREQUISITES
  • Understanding of trigonometric functions, specifically cosine and its inverse.
  • Familiarity with inverse trigonometric functions and their properties.
  • Basic knowledge of mathematical notation and functions.
  • Experience with angles in radians, particularly π/3.
NEXT STEPS
  • Research the properties of inverse trigonometric functions, focusing on their relationships.
  • Study the derivation and applications of acos in various mathematical contexts.
  • Learn about the unit circle and how it relates to trigonometric functions.
  • Explore the use of acos in solving real-world problems involving angles and distances.
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Mathematics students, educators, and anyone interested in deepening their understanding of trigonometric functions and their inverses.

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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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"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.
 
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!
 

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