MHB Can You Solve This Tricky Trigonometric Floor Function Equation?

AI Thread Summary
The discussion revolves around solving the equation involving the floor function and trigonometric functions: {sin(⌊x⌋)} + {cos(⌊x⌋)} = {tan(⌊x⌋)} for real solutions. Participants clarify that the notation {x} represents the fractional part of x, defined as x - ⌊x⌋. There is also a question about whether x is measured in radians or degrees, with confirmation that x is in radians. The thread emphasizes understanding the fractional part in the context of the equation. Overall, the focus is on finding real solutions to the given trigonometric equation.
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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