How Do You Solve the Inverse Function Problem Involving sin^(-1)(cos(7π/5))?

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SUMMARY

The discussion focuses on solving the inverse function problem involving the expression sin-1(cos(7π/5)). Participants clarify that the periodic nature of the cosine function, which has a period of 2π, is essential in determining the general solution. The equation x + n2π arises from the periodicity of the cosine function, indicating that multiple solutions exist for the inverse sine function. The conversation highlights the importance of understanding the relationship between trigonometric functions and their inverses.

PREREQUISITES
  • Understanding of trigonometric functions, specifically sine and cosine.
  • Knowledge of inverse trigonometric functions, particularly arcsin and its properties.
  • Familiarity with periodic functions and their implications in solving equations.
  • Basic algebra skills for manipulating equations involving trigonometric identities.
NEXT STEPS
  • Study the properties of inverse trigonometric functions, focusing on arcsin and arccos.
  • Learn about the periodicity of trigonometric functions, specifically the implications of 2π for cosine.
  • Explore solving trigonometric equations using identities and transformations.
  • Practice problems involving inverse functions and their graphical representations.
USEFUL FOR

Mathematics students, educators, and anyone interested in understanding trigonometric identities and inverse functions in depth.

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sin-(cos(7pi/5) (arcsin)

i have the equation (x+n2pi) but don't know where to go from their
 
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How did you get x+n2pi?
 
f(x + P) = f(x)
the periodic function of cosine is 2pi? no?
 
Karma said:
sin-(cos(7pi/5) (arcsin)

i have the equation (x+n2pi) but don't know where to go from their
What you've written makes no sense at all! What do you mean by
"sin-(cos(7pi/5) (arcsin)"?? And what does that have to do with an inverse function?
 

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