# COT

 Syntax COT (angle) Location QL ROM

This function returns the cotangent of a given angle (specified in radians).

In a right angled triangle the cotangent of an angle is defined as the ratio of the side adjoining the given angle to the side opposite to the given angle (forming a right angle with the other line). Due to the periodic nature of the function, it is best to work with angle in the range: 0 < angle < PI.

COT(angle) can also be calculated as COS(angle)/SIN(angle).

Example

A program to create a graph showing the range of the function COT:

```100 MODE 4: OPEN#1,con_448x200a32x16
110 SCALE 100,-75,-50
120 INK 4: LINE -75,0 TO 125,0: LINE 0,-50 TO 0,50
130 CURSOR 0,0,0,0: PRINT '0'
140 CURSOR 0,0,-100,0: PRINT '-ã'
150 CURSOR 0,0,100,0: PRINT 'ã'
160 CURSOR 0,0,-200,0: PRINT '-ã * 2'
170 CURSOR 0,0,200,0: PRINT '2ã'
180 CURSOR 0,0,0,-100: PRINT '1'
190 CURSOR 0,0,0,90: PRINT '-1'
200 INK 7
210 FOR ang=-(PI*2)+1E-2 TO PI*2 STEP 1E-2
220   POINT ang*75/(PI*2),50*COT(ang)
230 END FOR ang
```

NOTE 1

Although COT(PI) and COT(PI*x) should be undefined (values of angle very close to PI tend to infinity), on most QDOS implementations, it gives a very large positive or negative number.

Currently, only the Lightning maths package and SMS produce an overflow error (the correct result).

NOTE 2

On Minerva v1.96+ very large values of angle will return the value 0. On other implementations produce an overflow error.

NOTE 3

COT(0) on most ROMs gives 1 - this is fixed on Minerva, SMS, Lightning, QXL, and ST/QL which give an overflow error.

NOTE 4

COT(PI/2) should equal zero - on all implementations of this command, this returns a number near to zero (except under SMS).

CROSS-REFERENCE