About cosine function

[Sergio Tallone]

Hi,
could someone kindly explain to me why the simple code below give me a negative value for cosine of 90 degrees?

#COMPILE EXE
#DIM ALL

FUNCTION PBMAIN () AS LONG

  LOCAL angle AS extended
  
  angle = 0.0174532925199433## * 90
  
  PRINT USING$("#.##################",COS(angle))
  PRINT SGN(COS(angle))
  
  WAITKEY$

END FUNCTION

thanks!

Sergio

[Michael Mattias]

Output my system (PB/CC 5.0.0) :

-.000000000000000381
-1

Since cos(90 degrees ) is zero, seems to me you are simply running into the rounding inherent in the use of floating point numbers and an undisciplined use of PRINT

Of course you could try it this way...

FUNCTION PBMAIN () AS LONG

  LOCAL angle AS EXTENDED
  LOCAL pi AS EXTENDED

  angle = 0.0174532925199433## * 90

  PRINT USING$("#.##################",COS(angle))
  PRINT SGN(COS(angle))
  
  pi    =  ATN(1) * 4##
  PRINT    PI
  
  angle  = Pi/2.00##     '  90 degrees
  
  PRINT USING$("angle #.######  cosine  #.#######", angle, COS(angle))
 

  WAITKEY$

END FUNCTION

.. and get pretty much what you'd expect.

MCM

[Sergio Tallone]

Hi Michael,
tank you for the reply.
I'm aware of the rounding problems related to the storage capabilities of the different numeric data types.
IMHO the problem is related to the negative value, because checking the sign of trigonometric functions is useful in order to determine the trigonometric quadrant.
In geometric algorithms where the cosine function is used, this problem can create wrong results.

bye

Sergio

[Paul Dixon]

Sergio,
Try a more accurate value for pi/180

  angle = 0.01745329251994329577## * 90

Paul.

[Arthur Gomide]

Sergio,

Do not make checks to the exact values because the rounding errors may hinder such verifications, but check the proximity of data to desired values, like in

  value## = COS(angle)
  IF ABS(value##) <= 5e-16 THEN 'value## is near zero
      'do something when zero
  END IF

or try using the ROUND function

[Sergio Tallone]

Many thanks to all for the replies.
The Paul's suggestion worked fine.

Cheers

sergio

[Walter Henn]

Many thanks to all for the replies.
The Paul's suggestion worked fine.

sergio

Actually, Paul's approximation to Pi/2 radians is not as accurate as Michael's approximation -- 2 * ATN(1) -- which produces the closest possible value to Pi/2 that can be represented in the extended precision format. As such, it provides a significantly closer value to zero for its cosine than Paul's value.

Although Paul's approximation to Pi/2 results in a positive sign for the cosine (whereas Michael's approximation results in a negative sign), this is no more or less correct than a negative sign since the true sign of COS(Pi/2) is neither. Paul's approximation simply lands on a value that is slightly less than Pi/2, whereas Michael's lands on a value that is slightly more than Pi/2.

The main point of this post is that your PowerBASIC calculations will never come up with an angle such that COS(angle) = 0, since that angle is not representable in the extended precision format. The cosine of an angle will go from a positive value in the first quadrant directly to a negative value in the second quadrant without producing a value of zero (90 degrees).