Can You Solve This Tricky Trigonometric Floor Function Equation?

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SUMMARY

The discussion centers on solving the equation $\{ \sin \lfloor x \rfloor \}+\{ \cos \lfloor x \rfloor \}=\{ \tan \lfloor x \rfloor \}$ for real solutions. Participants clarify that the notation $\{ x \}$ represents the fractional part of $x$, defined as $\{ x \}=x-\lfloor x \rfloor$. The variable $x$ is specified to be in radians, which is crucial for solving the trigonometric functions involved.

PREREQUISITES
  • Understanding of the floor function and its notation
  • Knowledge of trigonometric functions: sine, cosine, and tangent
  • Familiarity with fractional parts of numbers
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the properties of the floor function in mathematical equations
  • Explore the behavior of trigonometric functions in radians
  • Learn about solving equations involving fractional parts
  • Investigate graphical methods for visualizing trigonometric equations
USEFUL FOR

Mathematicians, students studying trigonometry, and anyone interested in solving complex equations involving floor functions and fractional parts.

anemone
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Solve $\{ \sin \lfloor x \rfloor \}+\{ \cos \lfloor x \rfloor \}=\{ \tan \lfloor x \rfloor \}$ for real solution(s).
 
x in radian or degree ?
 
Hi Kali, $x$ is in radian.
 
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anemone said:
Solve $\{ \sin \lfloor x \rfloor \}+\{ \cos \lfloor x \rfloor \}=\{ \tan \lfloor x \rfloor \}$ for real solution(s).
Sorry, but I'm a bit confused. I know what the floor function does but what does the {.} do?

-Dan
 
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Sorry Dan for not being clear in my question.(Blush)

{} means the fractional part of $x$, and defined by the formula $\{ x \}=x-\lfloor x \rfloor$.

Hope this clears it up!
 

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