# TAN¶

 Syntax TAN (angle) angle <> (2n+1) * PI/2 (n=0,1,2,…) Location QL ROM

This function calculates the tangent of an angle given in radians. The solution of TAN(PI/2) is not actually defined because the definition of TAN is TAN(x)=SIN(x)/COS(x) and COS(PI/2)=0. In practice, most ROM implementations will return a value of about 1E10 instead of an error because they calculate COS(PI/2)<>0. Due to the periodic nature of this function function, values for angle should really be in the range -PI/2 < angle < PI/2.

Example

```100 WINDOW 448,200,32,16: PAPER 3: CLS
110 SCALE 8,-.2,-.2: INK 7
120 INPUT "Angle (0..90):"!angle
130 INPUT "Speed (..11 m/s):"!speed
150 c2=9.81 / 2 / speed^2 / COS(angle)^2
160 :
170 FOR x=0 TO c1/c2 STEP c1/c2/20
180   y=c1 * x - c2 * x^2
190   FILL 1: CIRCLE x,y,.2: FILL 0
200 END FOR x
```

NOTE 1

TAN(PI)==0 on all implementations - this should be zero. Only SMS currently corrects this.

NOTE 2

On Minerva v1.96+ large values of angle return 0. On other ROMs it produces an overflow error.

CROSS-REFERENCE

SIN, COS, COT, ASIN, ACOS, ATAN and ACOT are other common trigonometrical functions. RAD converts degrees into radians, DEG vice-versa. Please also refer to the Mathematics section of the Appendix.