MHB Sin Values of 87 and 89 Degrees

  • Thread starter Thread starter juantheron
  • Start date Start date
  • Tags Tags
    Degrees Sin
Click For Summary
The value of the product $\sin(1^\circ) \cdot \sin(3^\circ) \cdot \sin(5^\circ) \cdots \sin(87^\circ) \cdot \sin(89^\circ)$ is approximately \(4.0194366942304562 \times 10^{-14}\). Attempts to solve this algebraically have been unsuccessful, with some participants exploring complex numbers and nth roots of unity for potential solutions. A reference method involving cosine functions has been suggested to approach the problem. The discussion highlights the challenge of finding a straightforward algebraic solution. Overall, the focus remains on determining the value of the sine product.
juantheron
Messages
243
Reaction score
1
The value of $\sin (1^0).\sin (3^0).\sin (5^0)...\sin (87^0).\sin (89^0)$

where all angles are in degree
 
Mathematics news on Phys.org
jacks said:
The value of $\sin (1^0).\sin (3^0).\sin (5^0)...\sin (87^0).\sin (89^0)$

where all angles are in degree

Hi jacks,

I haven't found a way solve this algebraically. But if you are interested about the answer it is, \(4.0194366942304562\times 10^{-14}\)
 
Sudharaka said:
Hi jacks,

I haven't found a way solve this algebraically. But if you are interested about the answer it is, \(4.0194366942304562\times 10^{-14}\)

Thanks Sudhakara

I am trying to find it with the help of complex no.(like nth -roots of unity)
 
jacks said:
The value of $\sin (1^0).\sin (3^0).\sin (5^0)...\sin (87^0).\sin (89^0)$

where all angles are in degree
Follow the method used in http://www.mathhelpboards.com/showthread.php?253-Simplify-cos(a)cos(2a)cos(3a)-cos(999a)-if-a-(2pi)-1999&p=1517&viewfull=1#post1517, noting that $x=\pm1^\circ,\pm3^\circ,\pm5^\circ,\ldots,\pm89 ^\circ$ are the solutions of the equation $\cos(90x) = 0.$
 

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

MHB Evaluate the product of sines: sin1sin2sin3…sin89
  • · Replies 5 ·
Replies
5
Views
3K
MHB Finding x in Degrees: Solving a Quadratic Equation for Trigonometric Functions
  • · Replies 5 ·
Replies
5
Views
1K
Undergrad Transforming coordinates between Cartesian and spherical
  • · Replies 1 ·
Replies
1
Views
2K
MHB Prove Triangle Inequality: $\sqrt{2}\sin A-2\sin B+\sin C=0$
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Equation to graph a sine wave that acts like a point on a unit circle
  • · Replies 8 ·
Replies
8
Views
2K
MHB Graph of $y=\sin{x}-2$ on the domain $[0,2\pi]$
  • · Replies 2 ·
Replies
2
Views
1K
A Trick to Memorizing Trig Special Angle Values Table
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Determine ## \beta ## as a function of ##\theta## linkage
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Trig Manipulations I'm Not Getting
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Finding Minimal Mean Distance Curves on the Unit Sphere
  • · Replies 2 ·
Replies
2
Views
2K