MHB Can You Solve This Tricky Trigonometric Floor Function Equation?

Click For 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
Gold Member
MHB
POTW Director
Messages
3,851
Reaction score
115
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.
 
Mathematics news on Phys.org
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
 
Mathematics news on Phys.org
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!
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

Undergrad Solving an equation that contains the floor function
  • · Replies 9 ·
Replies
9
Views
3K
MHB Expressing First 1000 Positive Integers as Floor Functions
  • · Replies 3 ·
Replies
3
Views
1K
MHB Finding Real Solutions to the Floor Function Equation: A Scientific Approach
  • · Replies 5 ·
Replies
5
Views
2K
MHB Evaluating Definite Integrals with Floor Function
  • · Replies 1 ·
Replies
1
Views
2K
MHB What Values of \(a\) Satisfy the Equation Involving Floor Functions?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Can you prove the Floor Function Challenge?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Floor Function and Tangent function
  • · Replies 1 ·
Replies
1
Views
1K
MHB Solving equation of floor function
  • · Replies 2 ·
Replies
2
Views
2K
MHB Can You Prove the Floor Function Challenge for Real Numbers?
  • · Replies 4 ·
Replies
4
Views
2K
MHB Summation: trigonometric identity
  • · Replies 2 ·
Replies
2
Views
2K