TAN
TAN is a BASIC function which returns the Tangent of the angle (passed as a parameter).
Availability  Present in all original versions of BBC BASIC.  
Syntax  BASIC IV  <numvar> = TAN( <numeric>)

Token (hex)  BASIC IV  B7 (function)

Description  BASIC IV  Returns the Tangent of the angle (passed as a parameter) 
Associated keywords  SIN , COS , ATN , ASN , ACS

Contents 
Description
TAN
accepts a single parameter (the angle), and returns the Tangent of that angle.
Internal Operation
Overview
TAN(x)
To obtain the Tangent value the SIN(x) result is divided by the COS(x) result:
 TAN(x) = SIN(x) / COS(x)
Detailed
BASIC 4 implements TAN as follows:
The TAN routine calls &A93A to obtain the Floatingpoint argument and use continuedfraction expressions to calculate either the Sine or Cosine value (depending on the value of the argument) of the argument.
This FWA result is stored in temporary Floatingpoint location &047B&047F.
Call &A917 (SIN) to calculate the Sine value from the FWA result.
Store the Sine result in the temporary Floatingpoint location &0476&047A.
Set the FWA back to the &A93A result (from the Temporary Floatingpoint variable at &047B&047F).
Call &A915 (COS) to calculate the Cosine value from the &A93A result.
Note: Storing the &A93A value avoids the need to calculate it again!
Set the argument pointer to point to &0476 (the Sine result).
Call &A5EE to divide argp by the FWA [FWA = argp / FWA], where argp points to the Sine result and the FWA contains the Cosine result.
Dividing the Sine result by the Cosine result gives the Tangent value.
Exit with A = #&FF (as the result is Floatingpoint and is located in the FWA).
Example 1: TAN(90)
 Divide the SIN(90) result by the COS(90) result
 FWA = 0.8939945 / 0.4480777 > 1.9951774 (= the TAN result)
Example 2: TAN(2.41)
 Divide the SIN(2.41) result by the COS(2.41) result
 FWA = 0.6680554 / 0.7441115 > 0.8977893 (= the TAN result)
Example 3: TAN(1.5)
 Divide the SIN(1.5) result by the COS(1.5) result
 FWA = 0.9974949 / 0.0707372 > 14.1014191 (= the TAN result)
Example 4: TAN(5.63)
 Divide the SIN(5.63) result by the COS(5.63) result
 FWA = 0.6078147 / 0.7940788 > 0.7654337 (= the TAN result)
Example 5: TAN(0)
 Divide the SIN(0) result by the COS(0) result
 FWA = 0 / 1 > 0 (= the TAN result)
Example 6: TAN(0.75)
 Divide the SIN(0.75) result by the COS(0.75) result
 FWA = 0.6816387 / 0.7316889 > 0.9315963 (= the TAN result)
Example 7: TAN(0.25)
 Divide the SIN(0.25) result by the COS(0.25) result
 FWA = 0.2474039 / 0.9689124 > 0.2553418 (= the TAN result)
Kranser 23:11, 2 October 2007 (BST)